[{"data":1,"prerenderedAt":9347},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-datamining":1626,"course-stats-ipmrk":2838,"course-topics-ipmrk":2841,"backlinks-datamining":9324,"related-datamining":9340},{"courses":4,"counts":1622},[5,679,1148],{"id":6,"title":7,"body":8,"course":658,"courseName":659,"courses":659,"created":660,"description":641,"examInfo":659,"extension":661,"featured":662,"garant":659,"meta":663,"navigation":664,"path":665,"seo":666,"sources":667,"stem":669,"tags":670,"type":676,"updated":677,"__hash__":678},"courses\u002Fcourses\u002Fimork.md","Management oborových řešení (ImorK)",{"type":9,"value":10,"toc":640},"minimark",[11,15,114,119,147,151,193,197,202,251,255,338,342,371,375,395,399,455,459,533,537,548,552,604,608],[12,13,7],"h1",{"id":14},"management-oborových-řešení-imork",[16,17,18,29],"table",{},[19,20,21],"thead",{},[22,23,24,27],"tr",{},[25,26],"th",{},[25,28],{},[30,31,32,44,54,64,74,84,94,104],"tbody",{},[22,33,34,41],{},[35,36,37],"td",{},[38,39,40],"strong",{},"Zkratka",[35,42,43],{},"ImorK",[22,45,46,51],{},[35,47,48],{},[38,49,50],{},"Fakulta",[35,52,53],{},"Fakulta podnikatelská, VUT v Brně",[22,55,56,61],{},[35,57,58],{},[38,59,60],{},"Semestr",[35,62,63],{},"letní 2025\u002F2026",[22,65,66,71],{},[35,67,68],{},[38,69,70],{},"Ukončení",[35,72,73],{},"zkouška",[22,75,76,81],{},[35,77,78],{},[38,79,80],{},"Garant",[35,82,83],{},"Ing. Lukáš Novák, Ph.D.",[22,85,86,91],{},[35,87,88],{},[38,89,90],{},"Vyučující",[35,92,93],{},"Ing. Petr Sedlák",[22,95,96,101],{},[35,97,98],{},[38,99,100],{},"Ústav",[35,102,103],{},"Ústav informatiky",[22,105,106,111],{},[35,107,108],{},[38,109,110],{},"Prerekvizita",[35,112,113],{},"Management informační bezpečnosti (ImibePA)",[115,116,118],"h2",{"id":117},"cíle-předmětu","Cíle předmětu",[120,121,122,129,135,141],"ul",{},[123,124,125,126],"li",{},"Znalosti o specifických problémech a odlišnostech při ",[38,127,128],{},"oborovém řešení informační bezpečnosti",[123,130,131,132],{},"Porozumění jednotlivých řešení na úrovni ",[38,133,134],{},"případových studií",[123,136,137,138],{},"Přehled o rozdílných aspektech v závislosti na oborové řešení ",[38,139,140],{},"ISMS",[123,142,143,144],{},"Metodika pro budování bezpečných IS na bázi norem řady ",[38,145,146],{},"ISO\u002FIEC 27000",[115,148,150],{"id":149},"osnova","Osnova",[152,153,154,157,160,163,166,169,172,175,178,181,184,187,190],"ol",{},[123,155,156],{},"Bezpečnost v kyberprostoru",[123,158,159],{},"Budování bezpečnostního povědomí — SAE",[123,161,162],{},"Manažerská informační bezpečnost",[123,164,165],{},"Problematika GDPR",[123,167,168],{},"ISMS v ISVS",[123,170,171],{},"ISMS v univerzitním prostředí",[123,173,174],{},"ISMS ve zdravotnictví",[123,176,177],{},"ISMS v energetice",[123,179,180],{},"ISMS poskytovatelů konektivity (ISP)",[123,182,183],{},"Bezpečnost konvergovaných sítí",[123,185,186],{},"Řízení bezpečnosti www aplikací",[123,188,189],{},"Řízení bezpečnosti mailových aplikací",[123,191,192],{},"Řízení mobilní bezpečnosti",[115,194,196],{"id":195},"shrnutí-zdrojů","Shrnutí zdrojů",[198,199,201],"h3",{"id":200},"přednášky","Přednášky",[120,203,204,215,224,233,242],{},[123,205,206,214],{},[207,208,213],"a",{"className":209,"dataFsResolvedFilePath":211,"href":212},[210],"wikilink","summaries\u002Fimork-detail-predmetu.md","\u002Fwiki\u002Fimork-detail-predmetu","Detail předmětu"," — sylabus kurzu, hodnocení, literatura",[123,216,217,223],{},[207,218,222],{"className":219,"dataFsResolvedFilePath":220,"href":221},[210],"summaries\u002Fimork-manazerska-bezpecnost.md","\u002Fwiki\u002Fimork-manazerska-bezpecnost","Manažerská bezpečnost"," — governance, SIEM, log management, bezpečnostní role",[123,225,226,232],{},[207,227,231],{"className":228,"dataFsResolvedFilePath":229,"href":230},[210],"summaries\u002Fimork-bezpecnostni-strategie.md","\u002Fwiki\u002Fimork-bezpecnostni-strategie","Bezpečnostní strategie"," — tvorba a implementace bezpečnostní strategie",[123,234,235,241],{},[207,236,240],{"className":237,"dataFsResolvedFilePath":238,"href":239},[210],"summaries\u002Fimork-sae.md","\u002Fwiki\u002Fimork-sae","SAE"," — budování bezpečnostního povědomí (NIST SP 800-50\u002F16)",[123,243,244,250],{},[207,245,249],{"className":246,"dataFsResolvedFilePath":247,"href":248},[210],"summaries\u002Fimork-risk-management.md","\u002Fwiki\u002Fimork-risk-management","Risk Management"," — ISO 31000, ISO 27005, RTP, PoA\u002FSoA",[198,252,254],{"id":253},"oborová-isms","Oborová ISMS",[120,256,257,266,275,284,293,302,311,320,329],{},[123,258,259,265],{},[207,260,264],{"className":261,"dataFsResolvedFilePath":262,"href":263},[210],"summaries\u002Fimork-akademicke-prostredi.md","\u002Fwiki\u002Fimork-akademicke-prostredi","Akademické prostředí"," — kampus, WiFi, identita, VIS",[123,267,268,274],{},[207,269,273],{"className":270,"dataFsResolvedFilePath":271,"href":272},[210],"summaries\u002Fimork-financni-sektor.md","\u002Fwiki\u002Fimork-financni-sektor","Finanční sektor"," — DORA, MiCA, DLT\u002Fblockchain",[123,276,277,283],{},[207,278,282],{"className":279,"dataFsResolvedFilePath":280,"href":281},[210],"summaries\u002Fimork-zdravotnictvi.md","\u002Fwiki\u002Fimork-zdravotnictvi","Zdravotnictví"," — HIPAA, ISO 27799, PACS, DICOM, eHealth",[123,285,286,292],{},[207,287,291],{"className":288,"dataFsResolvedFilePath":289,"href":290},[210],"summaries\u002Fimork-energetika.md","\u002Fwiki\u002Fimork-energetika","Energetika"," — ISO 27019, IEC 61850, PLC\u002FSBC\u002FRTU",[123,294,295,301],{},[207,296,300],{"className":297,"dataFsResolvedFilePath":298,"href":299},[210],"summaries\u002Fimork-smart-grid.md","\u002Fwiki\u002Fimork-smart-grid","Smart Grid"," — NISTIR 7628, IEC 62351, prosumers",[123,303,304,310],{},[207,305,309],{"className":306,"dataFsResolvedFilePath":307,"href":308},[210],"summaries\u002Fimork-doprava.md","\u002Fwiki\u002Fimork-doprava","Doprava (železnice)"," — CLC\u002FTS 50701, kritická infrastruktura",[123,312,313,319],{},[207,314,318],{"className":315,"dataFsResolvedFilePath":316,"href":317},[210],"summaries\u002Fimork-automotive.md","\u002Fwiki\u002Fimork-automotive","Automotive"," — CAN bus, TISAX, UN Reg. 155",[123,321,322,328],{},[207,323,327],{"className":324,"dataFsResolvedFilePath":325,"href":326},[210],"summaries\u002Fimork-isp.md","\u002Fwiki\u002Fimork-isp","ISP\u002Ftelekomunikace"," — ISO 27011, NGN, 5G bezpečnost",[123,330,331,337],{},[207,332,336],{"className":333,"dataFsResolvedFilePath":334,"href":335},[210],"summaries\u002Fimork-mcn.md","\u002Fwiki\u002Fimork-mcn","Mission Critical Networks"," — NCPI, model hrozeb, dostupnost",[198,339,341],{"id":340},"bezpečnost-aplikací-a-dat","Bezpečnost aplikací a dat",[120,343,344,353,362],{},[123,345,346,352],{},[207,347,351],{"className":348,"dataFsResolvedFilePath":349,"href":350},[210],"summaries\u002Fimork-www.md","\u002Fwiki\u002Fimork-www","Bezpečnost webu"," — OWASP, SQL injection, XSS, Solid",[123,354,355,361],{},[207,356,360],{"className":357,"dataFsResolvedFilePath":358,"href":359},[210],"summaries\u002Fimork-email.md","\u002Fwiki\u002Fimork-email","Bezpečnost emailu"," — SPF, DKIM, DMARC, S\u002FMIME, šifrování",[123,363,364,370],{},[207,365,369],{"className":366,"dataFsResolvedFilePath":367,"href":368},[210],"summaries\u002Fimork-ochrana-dat.md","\u002Fwiki\u002Fimork-ochrana-dat","Ochrana dat"," — NAC, IDS\u002FIPS, SIEM, DLP, IPv6",[198,372,374],{"id":373},"kontinuita-a-obnova","Kontinuita a obnova",[120,376,377,386],{},[123,378,379,385],{},[207,380,384],{"className":381,"dataFsResolvedFilePath":382,"href":383},[210],"summaries\u002Fimork-bcm.md","\u002Fwiki\u002Fimork-bcm","BCM"," — ISO 22301, BIA, STEEPLE, PDCA",[123,387,388,394],{},[207,389,393],{"className":390,"dataFsResolvedFilePath":391,"href":392},[210],"summaries\u002Fimork-dr.md","\u002Fwiki\u002Fimork-dr","Disaster Recovery"," — RPO\u002FRTO, cloud DR, 7 tiers, DRaaS",[198,396,398],{"id":397},"kybernetické-útoky","Kybernetické útoky",[120,400,401,410,419,428,437,446],{},[123,402,403,409],{},[207,404,408],{"className":405,"dataFsResolvedFilePath":406,"href":407},[210],"summaries\u002Fimork-anatomie-utoku.md","\u002Fwiki\u002Fimork-anatomie-utoku","Anatomie útoku"," — APT, vektory, exploit\u002Fpayload",[123,411,412,418],{},[207,413,417],{"className":414,"dataFsResolvedFilePath":415,"href":416},[210],"summaries\u002Fimork-ai-utoky.md","\u002Fwiki\u002Fimork-ai-utoky","AI útoky"," — WormGPT, BEC, phishing",[123,420,421,427],{},[207,422,426],{"className":423,"dataFsResolvedFilePath":424,"href":425},[210],"summaries\u002Fimork-sitove-utoky.md","\u002Fwiki\u002Fimork-sitove-utoky","Síťové útoky"," — DDoS, spoofing, Emotet→Trickbot→Ryuk",[123,429,430,436],{},[207,431,435],{"className":432,"dataFsResolvedFilePath":433,"href":434},[210],"summaries\u002Fimork-ransomware.md","\u002Fwiki\u002Fimork-ransomware","Ransomware"," — historie 1989–2024, RaaS, NISTIR 8374, IR plán",[123,438,439,445],{},[207,440,444],{"className":441,"dataFsResolvedFilePath":442,"href":443},[210],"summaries\u002Fimork-rizeny-hacking.md","\u002Fwiki\u002Fimork-rizeny-hacking","Řízený hacking \u002F APT"," — APT skupiny, informační válka, OSINT",[123,447,448,454],{},[207,449,453],{"className":450,"dataFsResolvedFilePath":451,"href":452},[210],"summaries\u002Fimork-internetova-bezpecnost.md","\u002Fwiki\u002Fimork-internetova-bezpecnost","Internetová bezpečnost"," — kyberprostor, OSINT, behaviorální biometrika",[198,456,458],{"id":457},"případové-studie","Případové studie",[120,460,461,470,479,488,497,506,515,524],{},[123,462,463,469],{},[207,464,468],{"className":465,"dataFsResolvedFilePath":466,"href":467},[210],"summaries\u002Fimork-nemocnice.md","\u002Fwiki\u002Fimork-nemocnice","Útoky na nemocnice"," — Benešov (70M Kč), FN Brno (350M Kč), Nymburk",[123,471,472,478],{},[207,473,477],{"className":474,"dataFsResolvedFilePath":475,"href":476},[210],"summaries\u002Fimork-kradez-dat.md","\u002Fwiki\u002Fimork-kradez-dat","Krádež dat"," — PII, černý trh, IoT botnety, ISO 27701, GDPR",[123,480,481,487],{},[207,482,486],{"className":483,"dataFsResolvedFilePath":484,"href":485},[210],"summaries\u002Fimork-sprava-login.md","\u002Fwiki\u002Fimork-sprava-login","Správa login"," — privilegované účty, NIST SP 800-63, biometrika",[123,489,490,496],{},[207,491,495],{"className":492,"dataFsResolvedFilePath":493,"href":494},[210],"summaries\u002Fimork-ehealth.md","\u002Fwiki\u002Fimork-ehealth","eHealth"," — elektronizace zdravotnictví, telemedicína, NSeZ",[123,498,499,505],{},[207,500,504],{"className":501,"dataFsResolvedFilePath":502,"href":503},[210],"summaries\u002Fimork-tor.md","\u002Fwiki\u002Fimork-tor","TOR"," — anonymizace, onion routing, NSA X-Keyscore",[123,507,508,514],{},[207,509,513],{"className":510,"dataFsResolvedFilePath":511,"href":512},[210],"summaries\u002Fimork-payment.md","\u002Fwiki\u002Fimork-payment","Bezpečnost plateb"," — PCI DSS v4.0, NFC\u002Ftokenizace, EMV, darknet",[123,516,517,523],{},[207,518,522],{"className":519,"dataFsResolvedFilePath":520,"href":521},[210],"summaries\u002Fimork-mobilni-bezpecnost.md","\u002Fwiki\u002Fimork-mobilni-bezpecnost","Mobilní bezpečnost"," — SIMJaker, SIM swapping, 5G, Common Criteria",[123,525,526,532],{},[207,527,531],{"className":528,"dataFsResolvedFilePath":529,"href":530},[210],"summaries\u002Fimork-audio-hack.md","\u002Fwiki\u002Fimork-audio-hack","Audio Hack"," — fyzická zranitelnost HDD, CVE-2022-38392, rezonanční útok",[198,534,536],{"id":535},"další","Další",[120,538,539],{},[123,540,541,547],{},[207,542,546],{"className":543,"dataFsResolvedFilePath":544,"href":545},[210],"summaries\u002Fimork-digitalni-identita.md","\u002Fwiki\u002Fimork-digitalni-identita","Digitální identita a stopa"," — online identita, footprint",[115,549,551],{"id":550},"témata","Témata",[120,553,554,562,571,580,588,596],{},[123,555,556,561],{},[207,557,140],{"className":558,"dataFsResolvedFilePath":559,"href":560},[210],"topics\u002Fisms.md","\u002Fwiki\u002Fisms"," — systém řízení bezpečnosti informací",[123,563,564,570],{},[207,565,569],{"className":566,"dataFsResolvedFilePath":567,"href":568},[210],"topics\u002Frizeni-rizik.md","\u002Fwiki\u002Frizeni-rizik","Řízení rizik"," — proces identifikace a ošetření rizik",[123,572,573,579],{},[207,574,578],{"className":575,"dataFsResolvedFilePath":576,"href":577},[210],"topics\u002Fkyberneticka-bezpecnost.md","\u002Fwiki\u002Fkyberneticka-bezpecnost","Kybernetická bezpečnost"," — hrozby, útoky, obrana",[123,581,582,587],{},[207,583,240],{"className":584,"dataFsResolvedFilePath":585,"href":586},[210],"topics\u002Fsae.md","\u002Fwiki\u002Fsae"," — budování bezpečnostního povědomí",[123,589,590,595],{},[207,591,384],{"className":592,"dataFsResolvedFilePath":593,"href":594},[210],"topics\u002Fbcm.md","\u002Fwiki\u002Fbcm"," — řízení kontinuity činnosti",[123,597,598,603],{},[207,599,369],{"className":600,"dataFsResolvedFilePath":601,"href":602},[210],"topics\u002Fochrana-dat.md","\u002Fwiki\u002Fochrana-dat"," — technologická řešení ochrany",[115,605,607],{"id":606},"doporučená-literatura","Doporučená literatura",[120,609,610,618,625,631,634,637],{},[123,611,612,613,617],{},"JORDÁN, V. a ONDRÁK, V.: ",[614,615,616],"em",{},"Integrovaná podniková infrastruktura."," Brno: CERM, 2016. ISBN 978-80-214-5241-1",[123,619,620,621,624],{},"SEDLÁK, P. a KONEČNÝ, M.: ",[614,622,623],{},"Přeměna ISMS v manažerské informatice."," Brno: CERM, 2023. ISBN 978-80-7623-110-8",[123,626,620,627,630],{},[614,628,629],{},"Kybernetická (ne)bezpečnost."," Brno: CERM, 2021. ISBN 978-80-7623-068-2",[123,632,633],{},"ČSN EN ISO\u002FIEC 27011 — Bezpečnost pro telekomunikační organizace",[123,635,636],{},"ČSN EN ISO\u002FIEC 27019 — Bezpečnost pro energetický průmysl",[123,638,639],{},"ČSN EN ISO\u002FIEC 27799 — Bezpečnost ve zdravotnictví",{"title":641,"searchDepth":642,"depth":642,"links":643},"",2,[644,645,646,656,657],{"id":117,"depth":642,"text":118},{"id":149,"depth":642,"text":150},{"id":195,"depth":642,"text":196,"children":647},[648,650,651,652,653,654,655],{"id":200,"depth":649,"text":201},3,{"id":253,"depth":649,"text":254},{"id":340,"depth":649,"text":341},{"id":373,"depth":649,"text":374},{"id":397,"depth":649,"text":398},{"id":457,"depth":649,"text":458},{"id":535,"depth":649,"text":536},{"id":550,"depth":642,"text":551},{"id":606,"depth":642,"text":607},"imork",null,"2026-04-12","md",false,{},true,"\u002Fcourses\u002Fimork",{"title":7,"description":641},[668],"raw\u002Fimork\u002FDetail předmětu.md","courses\u002Fimork",[658,671,672,673,674,675],"isms","informacni-bezpecnost","kyberneticka-bezpecnost","oborova-reseni","iso-27000","course","2026-04-25","6MdSdXZJ3FNW9uPHrGzZPucQlKskWh23itOKhDSZfGs",{"id":680,"title":681,"body":682,"course":1128,"courseName":659,"courses":659,"created":1129,"description":641,"examInfo":659,"extension":661,"featured":662,"garant":659,"meta":1130,"navigation":664,"path":1131,"seo":1132,"sources":1133,"stem":1139,"tags":1140,"type":676,"updated":677,"__hash__":1147},"courses\u002Fcourses\u002Fimek.md","Matematická ekonomie (ImeK)",{"type":9,"value":683,"toc":1112},[684,687,719,723,731,735,738,748,831,841,861,871,947,951,962,966,969,994,1000,1011,1017,1020,1024,1061,1065,1068,1072],[12,685,681],{"id":686},"matematická-ekonomie-imek",[120,688,689,695,701,707,713],{},[123,690,691,694],{},[38,692,693],{},"Fakulta:"," FP VUT",[123,696,697,700],{},[38,698,699],{},"Garant:"," doc. RNDr. Bedřich Půža, CSc.",[123,702,703,706],{},[38,704,705],{},"Vyučující (kombinované studium):"," Mgr. Martina Bobalová, Ph.D.",[123,708,709,712],{},[38,710,711],{},"Ukončení:"," zkouška (písemná 60 min + ústní ~10 min)",[123,714,715,718],{},[38,716,717],{},"Semestr:"," letní 2025\u002F2026",[115,720,722],{"id":721},"cíl-předmětu","Cíl předmětu",[724,725,726,727,730],"p",{},"Hlouběji proniknout do kauzální podstaty ekonomických vztahů, rozvoj schopnosti vyjadřovat ekonomické vztahy ",[38,728,729],{},"exaktními prostředky"," a provádět jejich analýzy. Matematické modelování mikroekonomie a makroekonomie pomocí prostředků inženýrské matematiky (derivace, integrály, Lagrangeova metoda).",[115,732,734],{"id":733},"obsah-kurzu","Obsah kurzu",[724,736,737],{},"Kurz je v kombinovaném studiu rozčleněn do tří přednáškových bloků:",[198,739,741,742],{"id":740},"blok-1-kalkul-poptávkanabídka-příjemnákladyzisk","Blok 1 — ",[207,743,747],{"className":744,"dataFsResolvedFilePath":745,"href":746},[210],"summaries\u002Fimek-blok-01.md","\u002Fwiki\u002Fimek-blok-01","Kalkul, poptávka\u002Fnabídka, příjem\u002Fnáklady\u002Fzisk",[120,749,750,759,768,777,786,795,804,813,822],{},[123,751,752,758],{},[207,753,757],{"className":754,"dataFsResolvedFilePath":755,"href":756},[210],"topics\u002Fzaklady-matematicke-ekonomie.md","\u002Fwiki\u002Fzaklady-matematicke-ekonomie","Základy matematické ekonomie"," — model, endogenní\u002Fexogenní proměnné, ceteris paribus, komparativní statika",[123,760,761,767],{},[207,762,766],{"className":763,"dataFsResolvedFilePath":764,"href":765},[210],"topics\u002Fderivace.md","\u002Fwiki\u002Fderivace","Derivace, diferenciál a extrémy 1D"," — geometrická a inženýrská interpretace, mezní veličiny",[123,769,770,776],{},[207,771,775],{"className":772,"dataFsResolvedFilePath":773,"href":774},[210],"topics\u002Fintegral.md","\u002Fwiki\u002Fintegral","Integrál"," — neurčitý a určitý, rekonstrukce TR z MR a TC z MC",[123,778,779,785],{},[207,780,784],{"className":781,"dataFsResolvedFilePath":782,"href":783},[210],"topics\u002Ffunkce-vice-promennych.md","\u002Fwiki\u002Ffunkce-vice-promennych","Funkce více proměnných"," — parciální derivace, diferenciál 2D, implicitní funkce, volné extrémy",[123,787,788,794],{},[207,789,793],{"className":790,"dataFsResolvedFilePath":791,"href":792},[210],"topics\u002Flagrangeova-metoda.md","\u002Fwiki\u002Flagrangeova-metoda","Lagrangeova metoda"," — vázané extrémy, multiplikátor jako náklady příležitosti",[123,796,797,803],{},[207,798,802],{"className":799,"dataFsResolvedFilePath":800,"href":801},[210],"topics\u002Fpoptavka-nabidka.md","\u002Fwiki\u002Fpoptavka-nabidka","Poptávka, nabídka a tržní rovnováha"," — modely D a S, rovnováha, multiplikátory",[123,805,806,812],{},[207,807,811],{"className":808,"dataFsResolvedFilePath":809,"href":810},[210],"topics\u002Fzdaneni-trhu.md","\u002Fwiki\u002Fzdaneni-trhu","Zdanění trhu"," — daň výrobci vs. spotřebiteli, rozklad daňového břemene, ekvivalence",[123,814,815,821],{},[207,816,820],{"className":817,"dataFsResolvedFilePath":818,"href":819},[210],"topics\u002Fprebytek-spotrebitele-vyrobce.md","\u002Fwiki\u002Fprebytek-spotrebitele-vyrobce","Přebytek spotřebitele a výrobce"," — CS, PS, plochy pod\u002Fnad křivkami",[123,823,824,830],{},[207,825,829],{"className":826,"dataFsResolvedFilePath":827,"href":828},[210],"topics\u002Fprijem-naklady-zisk.md","\u002Fwiki\u002Fprijem-naklady-zisk","Příjem, náklady a zisk"," — TR, AR, MR, TC, AC, MC, body zvratu, konstrukce nabídky firmy",[198,832,834,835],{"id":833},"blok-2-elasticita-a-produkce","Blok 2 — ",[207,836,840],{"className":837,"dataFsResolvedFilePath":838,"href":839},[210],"summaries\u002Fimek-blok-02.md","\u002Fwiki\u002Fimek-blok-02","Elasticita a produkce",[120,842,843,852],{},[123,844,845,851],{},[207,846,850],{"className":847,"dataFsResolvedFilePath":848,"href":849},[210],"topics\u002Felasticita.md","\u002Fwiki\u002Felasticita","Cenová, křížová a důchodová elasticita"," (jedno- i vícefaktorový model)",[123,853,854,860],{},[207,855,859],{"className":856,"dataFsResolvedFilePath":857,"href":858},[210],"topics\u002Fprodukce.md","\u002Fwiki\u002Fprodukce","Produkční funkce"," — Cobb-Douglasova, CES, lineární, Leontiefova, izokvanty, MRTS, Eulerova věta",[198,862,864,865],{"id":863},"blok-3-užitečnost-a-národní-důchod","Blok 3 — ",[207,866,870],{"className":867,"dataFsResolvedFilePath":868,"href":869},[210],"summaries\u002Fimek-blok-03.md","\u002Fwiki\u002Fimek-blok-03","Užitečnost a národní důchod",[120,872,873,906,929,938],{},[123,874,875,881,882,905],{},[207,876,880],{"className":877,"dataFsResolvedFilePath":878,"href":879},[210],"topics\u002Fuzitecnost.md","\u002Fwiki\u002Fuzitecnost","Užitečnost"," — pojem, mezní užitečnost, Cobb-Douglasova ",[883,884,887],"span",{"className":885},[886],"katex",[888,889,891],"math",{"xmlns":890},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[892,893,894,901],"semantics",{},[895,896,897],"mrow",{},[898,899,900],"mi",{},"U",[902,903,900],"annotation",{"encoding":904},"application\u002Fx-tex",", indiferenční křivky, MRCS",[123,907,908,914,915,928],{},[207,909,913],{"className":910,"dataFsResolvedFilePath":911,"href":912},[210],"topics\u002Foptimalizace-spotrebitele.md","\u002Fwiki\u002Foptimalizace-spotrebitele","Optimalizace spotřebitele"," — Lagrangeova maximalizace ",[883,916,918],{"className":917},[886],[888,919,920],{"xmlns":890},[892,921,922,926],{},[895,923,924],{},[898,925,900],{},[902,927,900],{"encoding":904},", duální minimalizace výdajů, Marshallova\u002FHicksova poptávka",[123,930,931,937],{},[207,932,936],{"className":933,"dataFsResolvedFilePath":934,"href":935},[210],"topics\u002Fnarodni-duchod.md","\u002Fwiki\u002Fnarodni-duchod","Národní důchod"," — GNP, spotřeba\u002Fúspory, MPC\u002FMPS, modely C-I, C-I-G, C-I-G-X",[123,939,940,946],{},[207,941,945],{"className":942,"dataFsResolvedFilePath":943,"href":944},[210],"topics\u002Fis-lm.md","\u002Fwiki\u002Fis-lm","IS-LM analýza"," — simultánní rovnováha trhu zboží a peněz, fiskální\u002Fmonetární politika",[115,948,950],{"id":949},"reference-a-přehledy","Reference a přehledy",[120,952,953],{},[123,954,955,961],{},[207,956,960],{"className":957,"dataFsResolvedFilePath":958,"href":959},[210],"outputs\u002Fimek-vzorce-prehled.md","\u002Fwiki\u002Fimek-vzorce-prehled","Kompletní přehled vzorců"," — všechny klíčové vzorce kurzu v definičním tvaru, se zdrojem a intuicí. Referenční list pro přípravu na zkoušku.",[115,963,965],{"id":964},"hodnocení-zkoušky","Hodnocení zkoušky",[724,967,968],{},"Písemná část (60 min) — 4 úlohy:",[152,970,971,977,983,989],{},[123,972,973,974],{},"Rozhodovací úloha o ekonomické funkci — ",[38,975,976],{},"10 bodů",[123,978,979,980],{},"Definice, formulace vlastnosti, interpretace ekonomické veličiny — ",[38,981,982],{},"20 bodů",[123,984,985,986],{},"Výpočetní úloha — ",[38,987,988],{},"30 bodů",[123,990,985,991],{},[38,992,993],{},"40 bodů",[724,995,996,999],{},[38,997,998],{},"Dílčí podmínky"," (nutné pro A–E):",[120,1001,1002,1005,1008],{},[123,1003,1004],{},"≥ 11 bodů ze součtu úloh 1 a 2",[123,1006,1007],{},"≥ 10 bodů z úlohy 3",[123,1009,1010],{},"≥ 10 bodů z úlohy 4",[724,1012,1013,1016],{},[38,1014,1015],{},"Stupnice:"," A (90–100), B (80–89), C (70–79), D (60–69), E (50–59), F (0–49 nebo nesplnění podmínek).",[724,1018,1019],{},"Doporučeno mít kalkulátor.",[115,1021,1023],{"id":1022},"literatura","Literatura",[120,1025,1026,1033,1040,1047,1054],{},[123,1027,1028,1029,1032],{},"I. Mezník, ",[614,1030,1031],{},"Úvod do matematické ekonomie pro ekonomy",", FP VUT \u002F CERM, Brno 2017 (CZ)",[123,1034,1035,1036,1039],{},"A.C. Chiang, ",[614,1037,1038],{},"Fundamental Methods of Mathematical Economics",", McGraw-Hill, 1984",[123,1041,1042,1043,1046],{},"J.U. Koch, L.A. Ostrosky, ",[614,1044,1045],{},"Introduction to Mathematical Economics",", McGraw-Hill, 1994",[123,1048,1049,1050,1053],{},"C.J. McKenna, R. Rees, ",[614,1051,1052],{},"Economics: A Mathematical Introduction",", Oxford UP, 1992",[123,1055,1056,1057,1060],{},"J. Jacques, ",[614,1058,1059],{},"Mathematics for Economics and Business",", Addison-Wesley, 1995",[115,1062,1064],{"id":1063},"prerekvizity","Prerekvizity",[724,1066,1067],{},"Standardní kurz inženýrské matematiky, mikroekonomie a makroekonomie na bakalářské úrovni.",[115,1069,1071],{"id":1070},"přehled-zdrojů","Přehled zdrojů",[120,1073,1074,1082,1089,1096,1103],{},[123,1075,1076,1081],{},[207,1077,213],{"className":1078,"dataFsResolvedFilePath":1079,"href":1080},[210],"summaries\u002Fimek-detail-predmetu.md","\u002Fwiki\u002Fimek-detail-predmetu"," — sylabus a administrativní informace",[123,1083,1084,1088],{},[207,1085,1087],{"className":1086,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok"," — 57 stran, matematický aparát + mikroekonomie",[123,1090,1091,1095],{},[207,1092,1094],{"className":1093,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok"," — 19 stran, elasticita a produkce",[123,1097,1098,1102],{},[207,1099,1101],{"className":1100,"dataFsResolvedFilePath":868,"href":869},[210],"KS 3. blok"," — 25 stran, užitečnost a národní důchod",[123,1104,1105,1111],{},[207,1106,1110],{"className":1107,"dataFsResolvedFilePath":1108,"href":1109},[210],"summaries\u002Fimek-kniha.md","\u002Fwiki\u002Fimek-kniha","Kniha Mezník — Úvod do matematické ekonomie"," — naskenované kap. 2–7 (107 stran), kompletní teorie + Příklady + Úlohy k samostatnému řešení",{"title":641,"searchDepth":642,"depth":642,"links":1113},[1114,1115,1123,1124,1125,1126,1127],{"id":721,"depth":642,"text":722},{"id":733,"depth":642,"text":734,"children":1116},[1117,1119,1121],{"id":740,"depth":649,"text":1118},"Blok 1 — Kalkul, poptávka\u002Fnabídka, příjem\u002Fnáklady\u002Fzisk",{"id":833,"depth":649,"text":1120},"Blok 2 — Elasticita a produkce",{"id":863,"depth":649,"text":1122},"Blok 3 — Užitečnost a národní důchod",{"id":949,"depth":642,"text":950},{"id":964,"depth":642,"text":965},{"id":1022,"depth":642,"text":1023},{"id":1063,"depth":642,"text":1064},{"id":1070,"depth":642,"text":1071},"imek","2026-04-20",{},"\u002Fcourses\u002Fimek",{"title":681,"description":641},[1134,1135,1136,1137,1138],"raw\u002Fimek\u002FDetail předmětu.md","raw\u002Fimek\u002FKS_prvni_blok.pdf","raw\u002Fimek\u002FKS_druhy_blok.pdf","raw\u002Fimek\u002FKS_treti_blok.pdf","raw\u002Fimek\u002Fkniha_scanned\u002F","courses\u002Fimek",[1128,1141,1142,1143,1144,1145,1146],"ekonomie","mikroekonomie","makroekonomie","lagrange","derivace","integraly","x73RNX_N_uAS3i63VHeCgVFPJa4tJKL2z8kq4DIN24M",{"id":1149,"title":1150,"body":1151,"course":1601,"courseName":659,"courses":659,"created":1602,"description":641,"examInfo":659,"extension":661,"featured":662,"garant":659,"meta":1603,"navigation":664,"path":1604,"seo":1605,"sources":1606,"stem":1612,"tags":1613,"type":676,"updated":677,"__hash__":1621},"courses\u002Fcourses\u002Fipmrk.md","Pokročilé metody v rozhodování (IpmrK)",{"type":9,"value":1152,"toc":1593},[1153,1156,1230,1232,1235,1237,1321,1325,1354,1358,1423,1425,1474,1476],[12,1154,1150],{"id":1155},"pokročilé-metody-v-rozhodování-ipmrk",[16,1157,1158,1166],{},[19,1159,1160],{},[22,1161,1162,1164],{},[25,1163],{},[25,1165],{},[30,1167,1168,1177,1186,1195,1203,1211,1221],{},[22,1169,1170,1174],{},[35,1171,1172],{},[38,1173,40],{},[35,1175,1176],{},"IpmrK",[22,1178,1179,1183],{},[35,1180,1181],{},[38,1182,50],{},[35,1184,1185],{},"Fakulta podnikatelská VUT v Brně",[22,1187,1188,1192],{},[35,1189,1190],{},[38,1191,80],{},[35,1193,1194],{},"prof. Ing. Petr Dostál, CSc.",[22,1196,1197,1201],{},[35,1198,1199],{},[38,1200,100],{},[35,1202,103],{},[22,1204,1205,1209],{},[35,1206,1207],{},[38,1208,60],{},[35,1210,63],{},[22,1212,1213,1218],{},[35,1214,1215],{},[38,1216,1217],{},"Jazyk",[35,1219,1220],{},"čeština",[22,1222,1223,1227],{},[35,1224,1225],{},[38,1226,70],{},[35,1228,1229],{},"zkouška (písemný test 0–20 bodů, ECTS) + seminární práce (8–12 stran)",[115,1231,722],{"id":721},[724,1233,1234],{},"Seznámit se s pokročilými a nestandardními metodami analytických a simulačních technik v ekonomii a financích. Důraz na teorii i aplikaci do manažerské praxe.",[115,1236,150],{"id":149},[152,1238,1239,1242,1251,1257,1263,1271,1277,1285,1290,1298,1306,1315,1318],{},[123,1240,1241],{},"Úvod",[123,1243,1244,1250],{},[207,1245,1249],{"className":1246,"dataFsResolvedFilePath":1247,"href":1248},[210],"topics\u002Ffuzzy-logika.md","\u002Fwiki\u002Ffuzzy-logika","Fuzzy logika"," — teorie",[123,1252,1253,1256],{},[207,1254,1249],{"className":1255,"dataFsResolvedFilePath":1247,"href":1248},[210]," + aplikace — Excel",[123,1258,1259,1262],{},[207,1260,1249],{"className":1261,"dataFsResolvedFilePath":1247,"href":1248},[210]," — aplikace MATLAB",[123,1264,1265,1250],{},[207,1266,1270],{"className":1267,"dataFsResolvedFilePath":1268,"href":1269},[210],"topics\u002Fumele-neuronove-site.md","\u002Fwiki\u002Fumele-neuronove-site","Umělé neuronové sítě",[123,1272,1273,1276],{},[207,1274,1270],{"className":1275,"dataFsResolvedFilePath":1268,"href":1269},[210]," + aplikace MATLAB",[123,1278,1279,1250],{},[207,1280,1284],{"className":1281,"dataFsResolvedFilePath":1282,"href":1283},[210],"topics\u002Fgeneticke-algoritmy.md","\u002Fwiki\u002Fgeneticke-algoritmy","Genetické algoritmy",[123,1286,1287,1276],{},[207,1288,1284],{"className":1289,"dataFsResolvedFilePath":1282,"href":1283},[210],[123,1291,1292],{},[207,1293,1297],{"className":1294,"dataFsResolvedFilePath":1295,"href":1296},[210],"topics\u002Fteorie-chaosu.md","\u002Fwiki\u002Fteorie-chaosu","Teorie chaosu",[123,1299,1300],{},[207,1301,1305],{"className":1302,"dataFsResolvedFilePath":1303,"href":1304},[210],"topics\u002Fdatamining.md","\u002Fwiki\u002Fdatamining","Datamining",[123,1307,1308,1314],{},[207,1309,1313],{"className":1310,"dataFsResolvedFilePath":1311,"href":1312},[210],"topics\u002Fpredikce.md","\u002Fwiki\u002Fpredikce","Predikce",", kapitálový trh",[123,1316,1317],{},"Řízení výroby a řízení rizik",[123,1319,1320],{},"Rozhodování",[115,1322,1324],{"id":1323},"hodnocení","Hodnocení",[120,1326,1327,1333],{},[123,1328,1329,1332],{},[38,1330,1331],{},"Zkouška",": písemný test, 0–20 bodů. A: 20–18, B: 17–16, C: 15–14, D: 13–12, E: 11–10, F: 9–0.",[123,1334,1335,1338,1339,1343,1344,1348,1349,1353],{},[38,1336,1337],{},"Seminární práce",": 8–12 stran, individuální zaměření na problematiku z praxe, řešení pomocí ",[207,1340,1342],{"className":1341,"dataFsResolvedFilePath":1247,"href":1248},[210],"fuzzy logiky",", ",[207,1345,1347],{"className":1346,"dataFsResolvedFilePath":1268,"href":1269},[210],"umělých neuronových sítí"," nebo ",[207,1350,1352],{"className":1351,"dataFsResolvedFilePath":1282,"href":1283},[210],"genetických algoritmů",". Nutná úspěšná obhajoba.",[115,1355,1357],{"id":1356},"hlavní-témata","Hlavní témata",[120,1359,1360,1366,1372,1378,1387,1393,1402,1408,1417],{},[123,1361,1362,1365],{},[207,1363,1249],{"className":1364,"dataFsResolvedFilePath":1247,"href":1248},[210]," — modelování rozhodování s vágními pojmy",[123,1367,1368,1371],{},[207,1369,1270],{"className":1370,"dataFsResolvedFilePath":1268,"href":1269},[210]," — učení z dat, klasifikace, predikce",[123,1373,1374,1377],{},[207,1375,1284],{"className":1376,"dataFsResolvedFilePath":1282,"href":1283},[210]," — evoluční optimalizace",[123,1379,1380,1386],{},[207,1381,1385],{"className":1382,"dataFsResolvedFilePath":1383,"href":1384},[210],"topics\u002Fevolucni-algoritmy.md","\u002Fwiki\u002Fevolucni-algoritmy","Evoluční algoritmy"," — metaheuristiky, rojové algoritmy, prohledávací metody",[123,1388,1389,1392],{},[207,1390,1297],{"className":1391,"dataFsResolvedFilePath":1295,"href":1296},[210]," — nelineární dynamické systémy",[123,1394,1395,1401],{},[207,1396,1400],{"className":1397,"dataFsResolvedFilePath":1398,"href":1399},[210],"topics\u002Foptimalizace.md","\u002Fwiki\u002Foptimalizace","Optimalizace"," — hledání minima\u002Fmaxima, MATLAB Optimization Toolbox",[123,1403,1404,1407],{},[207,1405,1305],{"className":1406,"dataFsResolvedFilePath":1303,"href":1304},[210]," — dolování z dat, klastrování, rozhodovací stromy, Witness Miner",[123,1409,1410,1416],{},[207,1411,1415],{"className":1412,"dataFsResolvedFilePath":1413,"href":1414},[210],"topics\u002Fanfis.md","\u002Fwiki\u002Fanfis","ANFIS"," — hybridní propojení fuzzy logiky a neuronových sítí",[123,1418,1419,1422],{},[207,1420,1313],{"className":1421,"dataFsResolvedFilePath":1311,"href":1312},[210]," — prognózování časových řad v ekonomii a financích",[115,1424,607],{"id":606},[120,1426,1427,1434,1440,1447,1454,1460,1467],{},[123,1428,1429,1430,1433],{},"DOSTÁL, P. ",[614,1431,1432],{},"Pokročilé metody analýz a modelování v podnikatelství a veřejné správě",", CERM, 2008",[123,1435,1429,1436,1439],{},[614,1437,1438],{},"Advanced Decision making in Business and Public Services",", CERM, 2011",[123,1441,1442,1443,1446],{},"DOSTÁL, P., RAIS, K., SOJKA, Z. ",[614,1444,1445],{},"Pokročilé metody manažerského rozhodování",", Grada, 2005",[123,1448,1449,1450,1453],{},"ALTROCK, C. ",[614,1451,1452],{},"Fuzzy Logic & Neurofuzzy",", 1996",[123,1455,1456,1457,1453],{},"GATELY, E. ",[614,1458,1459],{},"Neural Network for Financial Forecasting",[123,1461,1462,1463,1466],{},"DAVIS, L. ",[614,1464,1465],{},"Handbook of Genetic Algorithms",", 1991",[123,1468,1469,1470,1473],{},"PETERS, E. ",[614,1471,1472],{},"Fractal Market Analysis",", 1994",[115,1475,196],{"id":195},[120,1477,1478,1486,1495,1504,1513,1522,1531,1540,1549,1557,1566,1575,1584],{},[123,1479,1480,1485],{},[207,1481,213],{"className":1482,"dataFsResolvedFilePath":1483,"href":1484},[210],"summaries\u002Fipmrk-detail-predmetu.md","\u002Fwiki\u002Fipmrk-detail-predmetu"," — základní informace o kurzu",[123,1487,1488,1494],{},[207,1489,1493],{"className":1490,"dataFsResolvedFilePath":1491,"href":1492},[210],"summaries\u002Fipmrk-fuzzy-excel.md","\u002Fwiki\u002Fipmrk-fuzzy-excel","Fuzzy logika — Excel"," — princip fuzzy logiky, funkce členství, pravidla, implementace",[123,1496,1497,1503],{},[207,1498,1502],{"className":1499,"dataFsResolvedFilePath":1500,"href":1501},[210],"summaries\u002Fipmrk-fuzzy-matlab.md","\u002Fwiki\u002Fipmrk-fuzzy-matlab","Fuzzy logika — MATLAB"," — architektura fuzzy systému, návrh modelu",[123,1505,1506,1512],{},[207,1507,1511],{"className":1508,"dataFsResolvedFilePath":1509,"href":1510},[210],"summaries\u002Fipmrk-nn-teorie.md","\u002Fwiki\u002Fipmrk-nn-teorie","Neuronové sítě — teorie"," — perceptron, aktivační funkce, backpropagation",[123,1514,1515,1521],{},[207,1516,1520],{"className":1517,"dataFsResolvedFilePath":1518,"href":1519},[210],"summaries\u002Fipmrk-nn-vypocet.md","\u002Fwiki\u002Fipmrk-nn-vypocet","Neuronové sítě — výpočet"," — ruční učení neuronu, vícevrstvé sítě, trénování",[123,1523,1524,1530],{},[207,1525,1529],{"className":1526,"dataFsResolvedFilePath":1527,"href":1528},[210],"summaries\u002Fipmrk-nn-aplikace.md","\u002Fwiki\u002Fipmrk-nn-aplikace","Neuronové sítě — aplikace"," — ANFIS, scoring, predikce, deep learning",[123,1532,1533,1539],{},[207,1534,1538],{"className":1535,"dataFsResolvedFilePath":1536,"href":1537},[210],"summaries\u002Fipmrk-ga-teorie.md","\u002Fwiki\u002Fipmrk-ga-teorie","Genetické algoritmy — teorie"," — chromozomy, selekce, křížení, mutace",[123,1541,1542,1548],{},[207,1543,1547],{"className":1544,"dataFsResolvedFilePath":1545,"href":1546},[210],"summaries\u002Fipmrk-ga-vyuziti.md","\u002Fwiki\u002Fipmrk-ga-vyuziti","Genetické algoritmy — využití"," — optimalizace, TSP, knapsack, klastrování",[123,1550,1551,1556],{},[207,1552,1297],{"className":1553,"dataFsResolvedFilePath":1554,"href":1555},[210],"summaries\u002Fipmrk-chaos.md","\u002Fwiki\u002Fipmrk-chaos"," — atraktory, fraktály, motýlí efekt, Hurstův exponent",[123,1558,1559,1565],{},[207,1560,1564],{"className":1561,"dataFsResolvedFilePath":1562,"href":1563},[210],"summaries\u002Fipmrk-kniha.md","\u002Fwiki\u002Fipmrk-kniha","Kniha — Pokročilé metody"," — celá učebnice, 7 kapitol, kontrolní otázky, nová témata (evoluční alg., optimalizace, datamining)",[123,1567,1568,1574],{},[207,1569,1573],{"className":1570,"dataFsResolvedFilePath":1571,"href":1572},[210],"summaries\u002Fipmrk-evolucni-algoritmy.md","\u002Fwiki\u002Fipmrk-evolucni-algoritmy","Evoluční algoritmy — principy a přehled"," — pseudokódy, vzorce SA\u002FTabu\u002FACO\u002FPSO\u002FDE\u002FSOMA\u002FAIS\u002FABC\u002FGSO",[123,1576,1577,1583],{},[207,1578,1582],{"className":1579,"dataFsResolvedFilePath":1580,"href":1581},[210],"summaries\u002Fipmrk-optimalizace.md","\u002Fwiki\u002Fipmrk-optimalizace","Optimalizace — MATLAB Optimization Toolbox"," — kompletní syntaxe fmincon\u002Ffminsearch\u002Flinprog\u002Fintlinprog\u002Fga",[123,1585,1586,1592],{},[207,1587,1591],{"className":1588,"dataFsResolvedFilePath":1589,"href":1590},[210],"summaries\u002Fipmrk-datamining.md","\u002Fwiki\u002Fipmrk-datamining","Datamining — techniky a nástroje"," — CRISP-DM, Link analýza, k-means, rozhodovací stromy, Apriori, Witness Miner, MATLAB kód",{"title":641,"searchDepth":642,"depth":642,"links":1594},[1595,1596,1597,1598,1599,1600],{"id":721,"depth":642,"text":722},{"id":149,"depth":642,"text":150},{"id":1323,"depth":642,"text":1324},{"id":1356,"depth":642,"text":1357},{"id":606,"depth":642,"text":607},{"id":195,"depth":642,"text":196},"ipmrk","2026-04-10",{},"\u002Fcourses\u002Fipmrk",{"title":1150,"description":641},[1607,1608,1609,1610,1611],"raw\u002Fipmrk\u002FDetail předmětu.md","raw\u002Fipmrk\u002Fkniha.md","raw\u002Fipmrk\u002Fevolucni-algoritmy-online.md","raw\u002Fipmrk\u002Foptimalizace-online.md","raw\u002Fipmrk\u002Fdatamining-online.md","courses\u002Fipmrk",[1601,1614,1615,1616,1617,1618,1619,1620],"fuzzy","neuronove-site","geneticke-algoritmy","evolucni-algoritmy","chaos","optimalizace","datamining","_iX_YpjZn-5NmPhFSn_DHNExx_u1xi12WJEbWAHjXpg",{"ipmrk":1623,"imork":1624,"imek":1625},25,41,21,{"page":1627,"collection":2837},{"id":1628,"title":1305,"body":1629,"course":1601,"courses":659,"created":2822,"description":1635,"extension":661,"meta":2823,"navigation":664,"path":2824,"seo":2825,"sources":2826,"stem":2827,"tags":2828,"type":2835,"updated":677,"__hash__":2836},"topics\u002Ftopics\u002Fdatamining.md",{"type":9,"value":1630,"toc":2798},[1631,1633,1636,1643,1662,1666,1689,1693,1719,1722,1726,1732,1742,1835,1845,1847,1851,1855,1862,1872,1877,1891,1896,1928,1933,1944,1946,1950,1956,1961,1967,1972,1998,2003,2008,2038,2042,2049,2054,2068,2073,2093,2099,2101,2105,2110,2114,2119,2125,2133,2138,2144,2151,2156,2162,2170,2175,2179,2235,2241,2243,2247,2254,2264,2268,2273,2279,2284,2290,2295,2301,2312,2316,2322,2327,2344,2346,2350,2356,2362,2373,2383,2388,2414,2420,2429,2431,2435,2441,2445,2453,2507,2518,2538,2542,2550,2570,2578,2598,2603,2618,2620,2624,2729,2733,2762,2766,2769,2778,2794],[12,1632,1305],{"id":1620},[724,1634,1635],{},"Datamining (dolování z dat) je sada automatizovaných postupů pro nalézání dosud neznámých vzorů a vztahů ve velkých databázích. Zastřešuje širokou škálu technik používaných v řadě odvětví. Rozvoj začal počátkem 90. let 20. století u bank specializovaných na kreditní karty, rozšířil se do pojišťovnictví, veřejných služeb, zásilkových služeb, energetiky, maloobchodu a dalších.",[724,1637,1638,1639,1642],{},"Datamining je analytický krok procesu ",[38,1640,1641],{},"KDD (Knowledge Discovery in Databases)",". Stojí na průsečíku tří disciplín: strojové učení + statistika + správa databází.",[724,1644,1645,1646,1343,1650,1343,1654,1343,1658,1661],{},"Souvisí s: ",[207,1647,1649],{"className":1648,"dataFsResolvedFilePath":1247,"href":1248},[210],"fuzzy-logika",[207,1651,1653],{"className":1652,"dataFsResolvedFilePath":1268,"href":1269},[210],"neuronové sítě",[207,1655,1657],{"className":1656,"dataFsResolvedFilePath":1383,"href":1384},[210],"evoluční algoritmy",[207,1659,1619],{"className":1660,"dataFsResolvedFilePath":1398,"href":1399},[210],".",[115,1663,1665],{"id":1664},"cíle-dataminingu","Cíle dataminingu",[120,1667,1668,1674,1680,1686],{},[123,1669,1670,1673],{},[38,1671,1672],{},"Zvýšení zisku"," — identifikace nových zákazníků a příležitostí",[123,1675,1676,1679],{},[38,1677,1678],{},"Snížení nákladů"," — efektivnější cílení a alokace zdrojů",[123,1681,1682,1685],{},[38,1683,1684],{},"Snížení rizika ztrát"," — odhalení rizikových zákazníků, predikce odchodu",[123,1687,1688],{},"Správný výrobek → správný zákazník → správné místo → správný čas",[115,1690,1692],{"id":1691},"praktické-aplikace","Praktické aplikace",[120,1694,1695,1701,1707,1713],{},[123,1696,1697,1700],{},[38,1698,1699],{},"Bankovnictví",": Fraud detection, credit scoring, churn prediction, segmentace zákazníků",[123,1702,1703,1706],{},[38,1704,1705],{},"Pojišťovnictví",": Detekce podvodných pojistných událostí, optimalizace pojistných sazeb",[123,1708,1709,1712],{},[38,1710,1711],{},"Retail",": Market basket analysis (Amazon), doporučovací systémy, rozmístění zboží",[123,1714,1715,1718],{},[38,1716,1717],{},"Energetika\u002Fprůmysl",": Prediktivní údržba, optimalizace spotřeby",[1720,1721],"hr",{},[115,1723,1725],{"id":1724},"proces-práce-s-daty-crisp-dm","Proces práce s daty — CRISP-DM",[724,1727,1728,1731],{},[38,1729,1730],{},"CRISP-DM"," (Cross-Industry Standard Process for Data Mining) je nejrozšířenější metodika — průzkumy ukazovaly 3–4× vyšší využití než konkurence.",[1733,1734,1739],"pre",{"className":1735,"code":1737,"language":1738},[1736],"language-text","Business Understanding → Data Understanding → Data Preparation\n        ↑                                             ↓\n   Deployment ← Evaluation ← Modeling ← (iterativně zpět)\n","text",[1740,1741,1737],"code",{"__ignoreMap":641},[16,1743,1744,1757],{},[19,1745,1746],{},[22,1747,1748,1751,1754],{},[25,1749,1750],{},"Fáze",[25,1752,1753],{},"Obsah",[25,1755,1756],{},"Poznámka",[30,1758,1759,1771,1783,1798,1811,1823],{},[22,1760,1761,1766,1769],{},[35,1762,1763],{},[38,1764,1765],{},"1. Business Understanding",[35,1767,1768],{},"Definice cílů, obchodní otázka, kritéria úspěchu",[35,1770],{},[22,1772,1773,1778,1781],{},[35,1774,1775],{},[38,1776,1777],{},"2. Data Understanding",[35,1779,1780],{},"Sběr dat, průzkum, kvalita, vhodnost pro analýzu",[35,1782],{},[22,1784,1785,1790,1793],{},[35,1786,1787],{},[38,1788,1789],{},"3. Data Preparation",[35,1791,1792],{},"Čištění, klasifikace, vzorkování, sumarizace, transformace",[35,1794,1795],{},[38,1796,1797],{},"50–80 % celkového úsilí",[22,1799,1800,1805,1808],{},[35,1801,1802],{},[38,1803,1804],{},"4. Modeling",[35,1806,1807],{},"Výběr a aplikace technik, kalibrace parametrů",[35,1809,1810],{},"Nejkratší, ale nejviditelnější",[22,1812,1813,1818,1821],{},[35,1814,1815],{},[38,1816,1817],{},"5. Evaluation",[35,1819,1820],{},"Ověření vůči obchodním cílům, metriky přesnosti",[35,1822],{},[22,1824,1825,1830,1833],{},[35,1826,1827],{},[38,1828,1829],{},"6. Deployment",[35,1831,1832],{},"Nasazení do produkce, monitoring, finální zpráva",[35,1834],{},[1836,1837,1838],"blockquote",{},[724,1839,1840,1841,1844],{},"Proces je ",[38,1842,1843],{},"iterativní"," — z každé fáze se lze vracet zpět.",[1720,1846],{},[115,1848,1850],{"id":1849},"klíčové-techniky-dataminingu","Klíčové techniky dataminingu",[198,1852,1854],{"id":1853},"link-analýza-analýza-vazeb","Link analýza (Analýza vazeb)",[724,1856,1857,1858,1861],{},"Technika zaměřená na vyhodnocování ",[38,1859,1860],{},"vztahů (vazeb)"," mezi entitami v síti, místo studia vlastností jednotlivých entit.",[724,1863,1864,1867,1868,1871],{},[38,1865,1866],{},"Princip:"," Data jako ",[38,1869,1870],{},"graf"," — uzly = entity (osoby, účty, produkty), hrany = vztahy nebo interakce.",[724,1873,1874],{},[38,1875,1876],{},"Typy přístupů:",[120,1878,1879,1882,1885,1888],{},[123,1880,1881],{},"Heuristické — rozhodovací pravidla z odborných znalostí",[123,1883,1884],{},"Šablonové — zpracování nestrukturovaných dat",[123,1886,1887],{},"Podobnostní — vážené skórování atributů",[123,1889,1890],{},"Statistické — lexikální statistika",[724,1892,1893],{},[38,1894,1895],{},"Příklady použití:",[120,1897,1898,1904,1910,1916,1922],{},[123,1899,1900,1903],{},[38,1901,1902],{},"Fraud detection"," — odhalování fraud rings (překrývající se adresy, telefony u různých žadatelů)",[123,1905,1906,1909],{},[38,1907,1908],{},"AML"," (Anti-Money Laundering) — praní peněz",[123,1911,1912,1915],{},[38,1913,1914],{},"FBI ViCAP"," — propojování trestných činů",[123,1917,1918,1921],{},[38,1919,1920],{},"Google PageRank"," — hodnocení stránek podle příchozích odkazů",[123,1923,1924,1927],{},[38,1925,1926],{},"Sociální sítě"," — detekce komunit, šíření vlivu, doporučení přátel",[724,1929,1930],{},[38,1931,1932],{},"Historický vývoj:",[152,1934,1935,1938,1941],{},[123,1936,1937],{},"Generace (1975): Ruční maticové grafy",[123,1939,1940],{},"Generace: Automatizované nástroje (IBM i2 Analyst's Notebook)",[123,1942,1943],{},"Generace: Automatická vizualizace napojená na datové zdroje",[1720,1945],{},[198,1947,1949],{"id":1948},"klastrování-clustering","Klastrování (Clustering)",[724,1951,1952,1955],{},[38,1953,1954],{},"Definice:"," Unsupervised learning — rozdělení dat do skupin (clusterů\u002Fshluků) tak, aby objekty uvnitř skupiny byly si co nejpodobnější a objekty z různých skupin co nejodlišnější. Kategorie předem neznáme — algoritmus je hledá sám.",[1957,1958,1960],"h4",{"id":1959},"k-means-algoritmus","K-means algoritmus",[724,1962,1963,1966],{},[38,1964,1965],{},"Minimalizuje:"," WCSS (Within-Cluster Sum of Squares) — vnitřní varianci clusterů.",[724,1968,1969],{},[38,1970,1971],{},"Kroky:",[152,1973,1974,1980,1986,1992],{},[123,1975,1976,1979],{},[38,1977,1978],{},"Inicializace"," — náhodně zvolit k centroidů (moderní: k-means++)",[123,1981,1982,1985],{},[38,1983,1984],{},"Přiřazení"," — každý bod přiřadit do nejbližšího centroidu (Euklidovská vzdálenost)",[123,1987,1988,1991],{},[38,1989,1990],{},"Aktualizace"," — přepočítat centroidy jako průměr přiřazených bodů",[123,1993,1994,1997],{},[38,1995,1996],{},"Opakování"," — dokud se přiřazení stabilizuje nebo max. iterace",[1836,1999,2000],{},[724,2001,2002],{},"Při různých spuštěních může dávat různé výsledky → doporučuje se spustit vícekrát.",[724,2004,2005],{},[38,2006,2007],{},"Výběr počtu clusterů k:",[120,2009,2010,2016,2022,2028],{},[123,2011,2012,2015],{},[38,2013,2014],{},"Elbow method"," — vynést WCSS vs. k, hledat „loket\"",[123,2017,2018,2021],{},[38,2019,2020],{},"Silhouette analysis"," — jak dobře bod pasuje do svého vs. sousedního clusteru (hodnoty 0–1)",[123,2023,2024,2027],{},[38,2025,2026],{},"Gap statistic"," — porovnání se vzdáleností náhodných dat",[123,2029,2030,2033,2034,2037],{},[38,2031,2032],{},"Davies-Bouldin Index"," — nižší = lepší; ",[38,2035,2036],{},"Calinski-Harabasz Index"," — vyšší = lepší",[1957,2039,2041],{"id":2040},"hierarchické-klastrování","Hierarchické klastrování",[724,2043,2044,2045,2048],{},"Vytváří ",[38,2046,2047],{},"dendrogram"," — stromovou strukturu zobrazující postupné slučování clusterů.",[724,2050,2051],{},[38,2052,2053],{},"Přístupy:",[120,2055,2056,2062],{},[123,2057,2058,2061],{},[38,2059,2060],{},"Agglomerativní (zdola nahoru)"," — každý bod = vlastní cluster, postupně slučovat",[123,2063,2064,2067],{},[38,2065,2066],{},"Divisivní (shora dolů)"," — jeden velký cluster, postupně dělit",[724,2069,2070],{},[38,2071,2072],{},"Metody výpočtu vzdálenosti (linkage):",[120,2074,2075,2081,2087],{},[123,2076,2077,2080],{},[38,2078,2079],{},"Ward"," — minimalizuje nárůst SSE; clustery ≈ stejné velikosti; nejčastěji doporučovaná",[123,2082,2083,2086],{},[38,2084,2085],{},"Complete"," — vzdálenost = maximum mezi body",[123,2088,2089,2092],{},[38,2090,2091],{},"Average"," — vzdálenost = průměr",[724,2094,2095,2098],{},[38,2096,2097],{},"Čtení dendrogramu:"," Hledat nejdelší vertikální úsečku nepřerušenou horizontálou — tam nakrájíme strom. Počet clusterů = počet průsečíků řezné linie s dendrogramem.",[1720,2100],{},[198,2102,2104],{"id":2103},"rozhodovací-stromy-decision-trees","Rozhodovací stromy (Decision Trees)",[724,2106,2107,2109],{},[38,2108,1954],{}," Model klasifikující data pomocí hierarchického větvení. Každý vnitřní uzel = test atributu; každá větev = výsledek testu; každý list = výsledná třída nebo hodnota.",[1957,2111,2113],{"id":2112},"míry-nečistoty-uzlu","Míry nečistoty uzlu",[724,2115,2116],{},[38,2117,2118],{},"Entropie:",[1733,2120,2123],{"className":2121,"code":2122,"language":1738},[1736],"H(S) = −Σ pᵢ × log₂(pᵢ)\n",[1740,2124,2122],{"__ignoreMap":641},[120,2126,2127,2130],{},[123,2128,2129],{},"H = 0 → čistý uzel (vše jedné třídy)",[123,2131,2132],{},"H = 1 → maximální smíšenost (binární, 50\u002F50)",[724,2134,2135],{},[38,2136,2137],{},"Informační zisk (Information Gain):",[1733,2139,2142],{"className":2140,"code":2141,"language":1738},[1736],"Gain(S, A) = H(S) − Σ (|Sᵥ| \u002F |S|) × H(Sᵥ)\n",[1740,2143,2141],{"__ignoreMap":641},[724,2145,2146,2147,2150],{},"Vybíráme atribut A s ",[38,2148,2149],{},"nejvyšším"," informačním ziskem.",[724,2152,2153],{},[38,2154,2155],{},"Giniho index (Gini Impurity):",[1733,2157,2160],{"className":2158,"code":2159,"language":1738},[1736],"Gini(S) = 1 − Σ pᵢ²\n",[1740,2161,2159],{"__ignoreMap":641},[120,2163,2164,2167],{},[123,2165,2166],{},"Gini = 0 → čistý uzel",[123,2168,2169],{},"Gini = 0,5 → maximální nečistota (binární)",[1836,2171,2172],{},[724,2173,2174],{},"Gini je výpočetně jednodušší (bez logaritmů) — prakticky dávají podobné výsledky.",[1957,2176,2178],{"id":2177},"algoritmy-rozhodovacích-stromů","Algoritmy rozhodovacích stromů",[16,2180,2181,2194],{},[19,2182,2183],{},[22,2184,2185,2188,2191],{},[25,2186,2187],{},"Algoritmus",[25,2189,2190],{},"Metrika",[25,2192,2193],{},"Vlastnosti",[30,2195,2196,2209,2222],{},[22,2197,2198,2203,2206],{},[35,2199,2200],{},[38,2201,2202],{},"ID3",[35,2204,2205],{},"Informační zisk (entropie)",[35,2207,2208],{},"Pouze kategorická data, bez prořezávání",[22,2210,2211,2216,2219],{},[35,2212,2213],{},[38,2214,2215],{},"C4.5",[35,2217,2218],{},"Gain ratio (normalizovaný)",[35,2220,2221],{},"Spojité proměnné, chybějící hodnoty, prořezávání",[22,2223,2224,2229,2232],{},[35,2225,2226],{},[38,2227,2228],{},"CART",[35,2230,2231],{},"Giniho index",[35,2233,2234],{},"Binární stromy, klasifikace i regrese, prořezávání",[724,2236,2237,2240],{},[38,2238,2239],{},"Prořezávání (pruning):"," Stromy mají tendenci přetrénovat se (overfitting). Pruning odstraňuje statisticky nevýznamné větve.",[1720,2242],{},[115,2244,2246],{"id":2245},"asociační-pravidla-apriori-algoritmus","Asociační pravidla — Apriori algoritmus",[724,2248,2249,2250,2253],{},"Hledá vzory souvýskytu v databázích transakcí. Typicky: ",[38,2251,2252],{},"market basket analysis"," — které produkty se kupují společně.",[724,2255,2256,2259,2260,2263],{},[38,2257,2258],{},"Formát pravidla:"," ",[1740,2261,2262],{},"{A} → {B}"," — „kdo koupí A, koupí i B\"",[198,2265,2267],{"id":2266},"klíčové-metriky","Klíčové metriky",[724,2269,2270],{},[38,2271,2272],{},"Support (podpora):",[1733,2274,2277],{"className":2275,"code":2276,"language":1738},[1736],"Support(A) = počet transakcí s A \u002F celkový počet transakcí\n",[1740,2278,2276],{"__ignoreMap":641},[724,2280,2281],{},[38,2282,2283],{},"Confidence (důvěra):",[1733,2285,2288],{"className":2286,"code":2287,"language":1738},[1736],"Confidence(A → B) = Support(A ∪ B) \u002F Support(A)\n",[1740,2289,2287],{"__ignoreMap":641},[724,2291,2292],{},[38,2293,2294],{},"Lift:",[1733,2296,2299],{"className":2297,"code":2298,"language":1738},[1736],"Lift(A → B) = Confidence(A → B) \u002F Support(B)\n",[1740,2300,2298],{"__ignoreMap":641},[120,2302,2303,2306,2309],{},[123,2304,2305],{},"Lift = 1 → A a B jsou nezávislé",[123,2307,2308],{},"Lift > 1 → pozitivní asociace (A zvyšuje pravděpodobnost B)",[123,2310,2311],{},"Lift \u003C 1 → negativní asociace",[198,2313,2315],{"id":2314},"princip-apriori","Princip Apriori",[724,2317,2318,2321],{},[38,2319,2320],{},"Anti-monotone property:"," Pokud množina A nesplňuje min. support, žádná její nadmnožina nemůže být frekventovaná → efektivní prořezávání prostoru hledání.",[724,2323,2324],{},[38,2325,2326],{},"Postup:",[152,2328,2329,2332,2335,2338,2341],{},[123,2330,2331],{},"Nastavit min_sup a min_conf",[123,2333,2334],{},"Najít frekventované 1-itemsety",[123,2336,2337],{},"Generovat kandidáty (k+1)-itemsetů z frekventovaných k-itemsetů",[123,2339,2340],{},"Prořezat nesplňující min_sup",[123,2342,2343],{},"Opakovat; pak generovat pravidla splňující min_conf",[1720,2345],{},[115,2347,2349],{"id":2348},"witness-miner-lanner-group","Witness Miner \u002F Lanner Group",[724,2351,2352,2355],{},[38,2353,2354],{},"Lanner Group Ltd"," — softwarová společnost, Birmingham (UK), 1996. Specializace na simulační software.",[724,2357,2358,2361],{},[38,2359,2360],{},"WITNESS"," — diskrétní simulační software od 1986. Integrován v produktech Oracle, SAP, IBM. Umožňuje:",[120,2363,2364,2367,2370],{},[123,2365,2366],{},"Modelování podnikových procesů a výrobních operací",[123,2368,2369],{},"3D modelování, diskrétní a stochastická simulace",[123,2371,2372],{},"Integraci s MS Excel, MS Access, ODBC, CAD",[724,2374,2375,2378,2379,2382],{},[38,2376,2377],{},"Witness Miner"," — označení pro integraci ",[38,2380,2381],{},"process mining"," technik (Disco\u002FFluxicon) se simulačním nástrojem WITNESS.",[724,2384,2385],{},[38,2386,2387],{},"Funkce analýzy ze simulačních dat:",[120,2389,2390,2396,2402,2408],{},[123,2391,2392,2395],{},[38,2393,2394],{},"Závislosti vstupů a výstupů"," — jaké kombinace vstupních parametrů vedou k jakým výstupům",[123,2397,2398,2401],{},[38,2399,2400],{},"Pravidla"," — extrakce rozhodovacích pravidel z chování simulovaného systému",[123,2403,2404,2407],{},[38,2405,2406],{},"Shluky (clustery)"," — seskupení podobných scénářů výsledků simulace",[123,2409,2410,2413],{},[38,2411,2412],{},"Statistiky\u002FKPI"," — exportovatelné do Excel",[724,2415,2416,2419],{},[38,2417,2418],{},"WITNESS Optimizer"," — využívá Simulated Annealing a Tabu Search pro optimalizaci parametrů.",[1836,2421,2422],{},[724,2423,2424,2425,2428],{},"Poznámka: Specifický modul \"Witness Miner\" není podrobně zdokumentován veřejně — pravděpodobně proprietární terminologie nebo starší funkce. Viz ",[207,2426,1657],{"className":2427,"dataFsResolvedFilePath":1383,"href":1384},[210]," pro principy SA a Tabu Search.",[1720,2430],{},[115,2432,2434],{"id":2433},"matlab-pro-datamining","MATLAB pro datamining",[724,2436,2437,2438,1661],{},"MATLAB nabízí funkce v rámci ",[38,2439,2440],{},"Statistics and Machine Learning Toolbox",[198,2442,2444],{"id":2443},"klastrování","Klastrování",[724,2446,2447],{},[38,2448,2449,2452],{},[1740,2450,2451],{},"kmeans"," — k-means:",[1733,2454,2458],{"className":2455,"code":2456,"language":2457,"meta":641,"style":641},"language-matlab shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","[idx, C] = kmeans(data, k);\n% idx = přiřazení bodů; C = centroidy (k×p matice)\n\n% S vizualizací:\n[idx, C] = kmeans(data, 2);\ngscatter(data(:,1), data(:,2), idx);\nhold on;\nplot(C(:,1), C(:,2), 'kx', 'MarkerSize', 15, 'LineWidth', 3);\n","matlab",[1740,2459,2460,2467,2472,2477,2483,2489,2495,2501],{"__ignoreMap":641},[883,2461,2464],{"class":2462,"line":2463},"line",1,[883,2465,2466],{},"[idx, C] = kmeans(data, k);\n",[883,2468,2469],{"class":2462,"line":642},[883,2470,2471],{},"% idx = přiřazení bodů; C = centroidy (k×p matice)\n",[883,2473,2474],{"class":2462,"line":649},[883,2475,2476],{"emptyLinePlaceholder":664},"\n",[883,2478,2480],{"class":2462,"line":2479},4,[883,2481,2482],{},"% S vizualizací:\n",[883,2484,2486],{"class":2462,"line":2485},5,[883,2487,2488],{},"[idx, C] = kmeans(data, 2);\n",[883,2490,2492],{"class":2462,"line":2491},6,[883,2493,2494],{},"gscatter(data(:,1), data(:,2), idx);\n",[883,2496,2498],{"class":2462,"line":2497},7,[883,2499,2500],{},"hold on;\n",[883,2502,2504],{"class":2462,"line":2503},8,[883,2505,2506],{},"plot(C(:,1), C(:,2), 'kx', 'MarkerSize', 15, 'LineWidth', 3);\n",[724,2508,2509],{},[38,2510,2511,2514,2515,2517],{},[1740,2512,2513],{},"linkage"," + ",[1740,2516,2047],{}," — hierarchické klastrování:",[1733,2519,2521],{"className":2455,"code":2520,"language":2457,"meta":641,"style":641},"Z = linkage(data, 'ward');      % vytvoří hierarchickou strukturu\ndendrogram(Z);                  % vizualizace\nclusters = cluster(Z, 'maxclust', 4);   % řez na 4 clustery\n",[1740,2522,2523,2528,2533],{"__ignoreMap":641},[883,2524,2525],{"class":2462,"line":2463},[883,2526,2527],{},"Z = linkage(data, 'ward');      % vytvoří hierarchickou strukturu\n",[883,2529,2530],{"class":2462,"line":642},[883,2531,2532],{},"dendrogram(Z);                  % vizualizace\n",[883,2534,2535],{"class":2462,"line":649},[883,2536,2537],{},"clusters = cluster(Z, 'maxclust', 4);   % řez na 4 clustery\n",[198,2539,2541],{"id":2540},"rozhodovací-stromy","Rozhodovací stromy",[724,2543,2544],{},[38,2545,2546,2549],{},[1740,2547,2548],{},"fitctree"," — trénování:",[1733,2551,2553],{"className":2455,"code":2552,"language":2457,"meta":641,"style":641},"Mdl = fitctree(X_train, Y_train);\nview(Mdl, 'Mode', 'graph');     % vizualizace stromu\nresubLoss(Mdl)                  % přesnost na trénovacích datech\n",[1740,2554,2555,2560,2565],{"__ignoreMap":641},[883,2556,2557],{"class":2462,"line":2463},[883,2558,2559],{},"Mdl = fitctree(X_train, Y_train);\n",[883,2561,2562],{"class":2462,"line":642},[883,2563,2564],{},"view(Mdl, 'Mode', 'graph');     % vizualizace stromu\n",[883,2566,2567],{"class":2462,"line":649},[883,2568,2569],{},"resubLoss(Mdl)                  % přesnost na trénovacích datech\n",[724,2571,2572],{},[38,2573,2574,2577],{},[1740,2575,2576],{},"predict"," — predikce:",[1733,2579,2581],{"className":2455,"code":2580,"language":2457,"meta":641,"style":641},"YPred = predict(Mdl, X_test);\naccuracy = sum(YPred == Y_test) \u002F numel(Y_test);\nfprintf('Přesnost: %.2f%%\\n', accuracy * 100);\n",[1740,2582,2583,2588,2593],{"__ignoreMap":641},[883,2584,2585],{"class":2462,"line":2463},[883,2586,2587],{},"YPred = predict(Mdl, X_test);\n",[883,2589,2590],{"class":2462,"line":642},[883,2591,2592],{},"accuracy = sum(YPred == Y_test) \u002F numel(Y_test);\n",[883,2594,2595],{"class":2462,"line":649},[883,2596,2597],{},"fprintf('Přesnost: %.2f%%\\n', accuracy * 100);\n",[724,2599,2600],{},[38,2601,2602],{},"Prevence overfittingu:",[1733,2604,2606],{"className":2455,"code":2605,"language":2457,"meta":641,"style":641},"Mdl = fitctree(X, Y, 'MaxNumSplits', 10);   % omezení hloubky\nMdl = fitctree(X, Y, 'MinLeafSize', 5);     % min. vzorků v listu\n",[1740,2607,2608,2613],{"__ignoreMap":641},[883,2609,2610],{"class":2462,"line":2463},[883,2611,2612],{},"Mdl = fitctree(X, Y, 'MaxNumSplits', 10);   % omezení hloubky\n",[883,2614,2615],{"class":2462,"line":642},[883,2616,2617],{},"Mdl = fitctree(X, Y, 'MinLeafSize', 5);     % min. vzorků v listu\n",[1720,2619],{},[115,2621,2623],{"id":2622},"přehled-technik-pro-zkoušku","Přehled technik pro zkoušku",[16,2625,2626,2639],{},[19,2627,2628],{},[22,2629,2630,2633,2636],{},[25,2631,2632],{},"Technika",[25,2634,2635],{},"Co dělá",[25,2637,2638],{},"Klíčové pojmy",[30,2640,2641,2654,2667,2679,2691,2704,2716],{},[22,2642,2643,2648,2651],{},[35,2644,2645],{},[38,2646,2647],{},"Link analýza",[35,2649,2650],{},"Hledá vazby v síti entit",[35,2652,2653],{},"Graf, uzly, hrany, fraud detection",[22,2655,2656,2661,2664],{},[35,2657,2658],{},[38,2659,2660],{},"K-means",[35,2662,2663],{},"Seskupuje podobné objekty",[35,2665,2666],{},"Centroid, WCSS, Elbow method, k",[22,2668,2669,2673,2676],{},[35,2670,2671],{},[38,2672,2041],{},[35,2674,2675],{},"Stromová struktura podobnosti",[35,2677,2678],{},"Dendrogram, Ward, linkage",[22,2680,2681,2685,2688],{},[35,2682,2683],{},[38,2684,2541],{},[35,2686,2687],{},"Klasifikace větvícím se stromem",[35,2689,2690],{},"Entropie, informační zisk, Gini, ID3\u002FC4.5\u002FCART",[22,2692,2693,2698,2701],{},[35,2694,2695],{},[38,2696,2697],{},"Asociační pravidla",[35,2699,2700],{},"Vzory souvýskytu",[35,2702,2703],{},"Support, Confidence, Lift, Apriori",[22,2705,2706,2710,2713],{},[35,2707,2708],{},[38,2709,1730],{},[35,2711,2712],{},"Standardní proces projektu",[35,2714,2715],{},"6 fází, iterativní",[22,2717,2718,2723,2726],{},[35,2719,2720],{},[38,2721,2722],{},"WITNESS\u002FLanner",[35,2724,2725],{},"Simulace + process mining",[35,2727,2728],{},"Diskrétní simulace, KPIs, Optimizer",[115,2730,2732],{"id":2731},"kontrolní-otázky-ke-zkoušce","Kontrolní otázky ke zkoušce",[152,2734,2735,2738,2741,2744,2747,2750,2753,2756,2759],{},[123,2736,2737],{},"Čím se zabývá datamining?",[123,2739,2740],{},"Jak jsou data získávána?",[123,2742,2743],{},"Jak jsou data zpracovávána?",[123,2745,2746],{},"K čemu nám slouží datamining?",[123,2748,2749],{},"Co znamená Link analýza?",[123,2751,2752],{},"K čemu slouží klastrování?",[123,2754,2755],{},"K čemu slouží a co je to rozhodovací strom?",[123,2757,2758],{},"Jak lze využít programu MATLAB v dataminingu?",[123,2760,2761],{},"K čemu slouží program Witness Miner?",[115,2763,2765],{"id":2764},"pojmy-k-zapamatování","Pojmy k zapamatování",[724,2767,2768],{},"Datamining, zpracování dat, MATLAB, Witness Miner, závislosti vstupů a výstupů, volba pravidel, shluky, statistické charakteristiky.",[115,2770,2772,2773],{"id":2771},"zdroje-v-kurzu-ipmrk","Zdroje v kurzu ",[207,2774,1176],{"className":2775,"dataFsResolvedFilePath":2776,"href":2777},[210],"courses\u002Fipmrk.md","\u002Fwiki\u002Fipmrk",[120,2779,2780,2787],{},[123,2781,2782,2786],{},[207,2783,2785],{"className":2784,"dataFsResolvedFilePath":1562,"href":1563},[210],"Kniha"," — definice, shrnutí, kontrolní otázky, pojmy",[123,2788,2789,2793],{},[207,2790,2792],{"className":2791,"dataFsResolvedFilePath":1589,"href":1590},[210],"Techniky a nástroje"," — CRISP-DM, Link analýza, k-means, rozhodovací stromy, Apriori, Witness Miner, MATLAB kód (Wikipedia, GeeksforGeeks, IBM, Lanner)",[2795,2796,2797],"style",{},"html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":641,"searchDepth":642,"depth":642,"links":2799},[2800,2801,2802,2803,2808,2812,2813,2817,2818,2819,2820],{"id":1664,"depth":642,"text":1665},{"id":1691,"depth":642,"text":1692},{"id":1724,"depth":642,"text":1725},{"id":1849,"depth":642,"text":1850,"children":2804},[2805,2806,2807],{"id":1853,"depth":649,"text":1854},{"id":1948,"depth":649,"text":1949},{"id":2103,"depth":649,"text":2104},{"id":2245,"depth":642,"text":2246,"children":2809},[2810,2811],{"id":2266,"depth":649,"text":2267},{"id":2314,"depth":649,"text":2315},{"id":2348,"depth":642,"text":2349},{"id":2433,"depth":642,"text":2434,"children":2814},[2815,2816],{"id":2443,"depth":649,"text":2444},{"id":2540,"depth":649,"text":2541},{"id":2622,"depth":642,"text":2623},{"id":2731,"depth":642,"text":2732},{"id":2764,"depth":642,"text":2765},{"id":2771,"depth":642,"text":2821},"Zdroje v kurzu IpmrK","2026-04-16",{},"\u002Ftopics\u002Fdatamining",{"title":1305,"description":1635},[1608,1611],"topics\u002Fdatamining",[1601,1620,2829,2830,2831,2832,2833,2834],"crisp-dm","link-analyza","klastrovani","rozhodovaci-stromy","apriori","witness-miner","topic","PUkq0tAb0hdh4jBddhFDQLtfyJlrKVogvd_v45wMY5w","topics",{"zapisku":1623,"topics":2839,"summaries":2840,"outputs":2463},11,13,[2842,2952,3062,3931,4963,5197,5536,7205,8467,8637,8967],{"id":2843,"title":2844,"body":2845,"course":659,"courses":2941,"created":1602,"description":641,"extension":661,"meta":2942,"navigation":664,"path":2943,"seo":2944,"sources":2945,"stem":2947,"tags":2948,"type":2835,"updated":677,"__hash__":2951},"topics\u002Ftopics\u002Fanfis.md","ANFIS — Adaptive Neuro-Fuzzy Inference System",{"type":9,"value":2846,"toc":2934},[2847,2850,2859,2872,2876,2897,2901,2912,2919,2922,2926],[12,2848,2844],{"id":2849},"anfis-adaptive-neuro-fuzzy-inference-system",[724,2851,2852],{},[2853,2854],"img",{"alt":2855,"className":2856,"src":2858},"anfis-architektura",[210,2857],"wikilink-broken","\u002Fwiki-assets\u002Fanfis-architektura.jpeg",[724,2860,2861,2862,2866,2867,2871],{},"Hybridní přístup propojující ",[207,2863,2865],{"className":2864,"dataFsResolvedFilePath":1247,"href":1248},[210],"fuzzy logiku"," a ",[207,2868,2870],{"className":2869,"dataFsResolvedFilePath":1268,"href":1269},[210],"umělé neuronové sítě",". Spojuje výhody obou světů.",[115,2873,2875],{"id":2874},"princip","Princip",[120,2877,2878,2888],{},[123,2879,2880,2883,2884,2887],{},[38,2881,2882],{},"Od fuzzy logiky"," přebírá: pravidla KDYŽ–POTOM, jazykové proměnné, funkce členství → ",[38,2885,2886],{},"interpretovatelnost"," (model dává lidský smysl)",[123,2889,2890,2893,2894],{},[38,2891,2892],{},"Od neuronových sítí"," přebírá: schopnost učit se z dat, automatická úprava parametrů → ",[38,2895,2896],{},"adaptivnost",[115,2898,2900],{"id":2899},"kdy-je-anfis-vhodný","Kdy je ANFIS vhodný",[120,2902,2903,2906,2909],{},[123,2904,2905],{},"Chceme model srozumitelný člověku (na rozdíl od čisté neuronové sítě)",[123,2907,2908],{},"Nechceme vše nastavovat ručně (na rozdíl od čistého fuzzy systému)",[123,2910,2911],{},"Máme data i expertní znalost",[115,2913,2915,2916],{"id":2914},"význam-v-kurzu-ipmrk","Význam v kurzu ",[207,2917,1176],{"className":2918,"dataFsResolvedFilePath":2776,"href":2777},[210],[724,2920,2921],{},"ANFIS je klíčový styčný bod kurzu — propojuje dva hlavní bloky (fuzzy logika a neuronové sítě) do jednoho systému. Zkouškově důležité.",[115,2923,2925],{"id":2924},"zdroje","Zdroje",[120,2927,2928],{},[123,2929,2930,2933],{},[207,2931,1529],{"className":2932,"dataFsResolvedFilePath":1527,"href":1528},[210]," — ANFIS je zde představen",{"title":641,"searchDepth":642,"depth":642,"links":2935},[2936,2937,2938,2940],{"id":2874,"depth":642,"text":2875},{"id":2899,"depth":642,"text":2900},{"id":2914,"depth":642,"text":2939},"Význam v kurzu IpmrK",{"id":2924,"depth":642,"text":2925},[1601],{},"\u002Ftopics\u002Fanfis",{"title":2844,"description":641},[2946],"raw\u002Fipmrk\u002Fnn-aplikace.md","topics\u002Fanfis",[1601,2949,1614,1615,2950],"anfis","hybridni-system","w3x8TjfldoFMelvK-RKRrgErKY5CwNSfUH40UpDM_M4",{"id":2953,"title":2954,"body":2955,"course":659,"courses":3049,"created":1602,"description":3050,"extension":661,"meta":3051,"navigation":664,"path":3052,"seo":3053,"sources":3054,"stem":3057,"tags":3058,"type":2835,"updated":677,"__hash__":3061},"topics\u002Ftopics\u002Fbackpropagation.md","Backpropagation (zpětné šíření chyby)",{"type":9,"value":2956,"toc":3044},[2957,2960,2967,2971,3002,3006,3020,3024],[12,2958,2954],{"id":2959},"backpropagation-zpětné-šíření-chyby",[724,2961,2962,2963,1661],{},"Základní a nejdůležitější algoritmus učení vícevrstvých ",[207,2964,2966],{"className":2965,"dataFsResolvedFilePath":1268,"href":1269},[210],"neuronových sítí",[115,2968,2970],{"id":2969},"postup","Postup",[152,2972,2973,2979,2985,2991,2997],{},[123,2974,2975,2978],{},[38,2976,2977],{},"Dopředný průchod"," — síť spočítá výstup z aktuálních vah",[123,2980,2981,2984],{},[38,2982,2983],{},"Výpočet chyby"," — porovnání skutečného výstupu s cílem (e = y − m)",[123,2986,2987,2990],{},[38,2988,2989],{},"Zpětné šíření"," — chyba se šíří zpět přes vrstvy, určuje příspěvek každé váhy k chybě",[123,2992,2993,2996],{},[38,2994,2995],{},"Úprava vah"," — w_new = w_old + η · e · x (η = učicí koeficient)",[123,2998,2999,3001],{},[38,3000,1996],{}," — celý cyklus se opakuje přes trénovací data, dokud chyba neklesne pod mez",[115,3003,3005],{"id":3004},"klíčové-vlastnosti","Klíčové vlastnosti",[120,3007,3008,3011,3014,3017],{},[123,3009,3010],{},"Iterativní proces — jedna iterace nestačí",[123,3012,3013],{},"Učicí koeficient (learning rate) řídí velikost kroků",[123,3015,3016],{},"Příliš velký → nestabilita, příliš malý → pomalé učení",[123,3018,3019],{},"Může uváznout v lokálním minimu",[115,3021,3023],{"id":3022},"souvislosti","Souvislosti",[120,3025,3026,3032,3038],{},[123,3027,3028,3031],{},[207,3029,1270],{"className":3030,"dataFsResolvedFilePath":1268,"href":1269},[210]," — backpropagation je jejich hlavní učicí mechanismus",[123,3033,3034,3037],{},[207,3035,1511],{"className":3036,"dataFsResolvedFilePath":1509,"href":1510},[210]," — zde je backpropagation zaveden",[123,3039,3040,3043],{},[207,3041,1520],{"className":3042,"dataFsResolvedFilePath":1518,"href":1519},[210]," — ruční demonstrace principu",{"title":641,"searchDepth":642,"depth":642,"links":3045},[3046,3047,3048],{"id":2969,"depth":642,"text":2970},{"id":3004,"depth":642,"text":3005},{"id":3022,"depth":642,"text":3023},[1601],"Základní a nejdůležitější algoritmus učení vícevrstvých neuronových sítí.",{},"\u002Ftopics\u002Fbackpropagation",{"title":2954,"description":3050},[3055,3056],"raw\u002Fipmrk\u002Fnn-teorie.md","raw\u002Fipmrk\u002Fnn-vypocet.md","topics\u002Fbackpropagation",[1601,3059,1615,3060],"backpropagation","uceni","p2r9NLMc5uEQNYcZ19-gTHFKa1wYriITtRQEGsTyZmE",{"id":1628,"title":1305,"body":3063,"course":1601,"courses":659,"created":2822,"description":1635,"extension":661,"meta":3927,"navigation":664,"path":2824,"seo":3928,"sources":3929,"stem":2827,"tags":3930,"type":2835,"updated":677,"__hash__":2836},{"type":9,"value":3064,"toc":3904},[3065,3067,3069,3073,3087,3089,3105,3107,3125,3127,3129,3133,3138,3214,3220,3222,3224,3226,3230,3236,3240,3250,3254,3276,3280,3288,3290,3292,3296,3298,3302,3306,3324,3328,3332,3352,3354,3358,3362,3372,3376,3390,3394,3396,3398,3402,3404,3408,3413,3419,3423,3428,3432,3436,3441,3447,3451,3453,3497,3501,3503,3505,3509,3515,3517,3521,3526,3530,3535,3539,3544,3552,3554,3558,3562,3574,3576,3578,3582,3586,3594,3600,3604,3622,3626,3633,3635,3637,3641,3643,3649,3685,3693,3709,3711,3717,3733,3739,3755,3759,3771,3773,3775,3859,3861,3881,3883,3885,3890,3902],[12,3066,1305],{"id":1620},[724,3068,1635],{},[724,3070,1638,3071,1642],{},[38,3072,1641],{},[724,3074,1645,3075,1343,3078,1343,3081,1343,3084,1661],{},[207,3076,1649],{"className":3077,"dataFsResolvedFilePath":1247,"href":1248},[210],[207,3079,1653],{"className":3080,"dataFsResolvedFilePath":1268,"href":1269},[210],[207,3082,1657],{"className":3083,"dataFsResolvedFilePath":1383,"href":1384},[210],[207,3085,1619],{"className":3086,"dataFsResolvedFilePath":1398,"href":1399},[210],[115,3088,1665],{"id":1664},[120,3090,3091,3095,3099,3103],{},[123,3092,3093,1673],{},[38,3094,1672],{},[123,3096,3097,1679],{},[38,3098,1678],{},[123,3100,3101,1685],{},[38,3102,1684],{},[123,3104,1688],{},[115,3106,1692],{"id":1691},[120,3108,3109,3113,3117,3121],{},[123,3110,3111,1700],{},[38,3112,1699],{},[123,3114,3115,1706],{},[38,3116,1705],{},[123,3118,3119,1712],{},[38,3120,1711],{},[123,3122,3123,1718],{},[38,3124,1717],{},[1720,3126],{},[115,3128,1725],{"id":1724},[724,3130,3131,1731],{},[38,3132,1730],{},[1733,3134,3136],{"className":3135,"code":1737,"language":1738},[1736],[1740,3137,1737],{"__ignoreMap":641},[16,3139,3140,3150],{},[19,3141,3142],{},[22,3143,3144,3146,3148],{},[25,3145,1750],{},[25,3147,1753],{},[25,3149,1756],{},[30,3151,3152,3162,3172,3184,3194,3204],{},[22,3153,3154,3158,3160],{},[35,3155,3156],{},[38,3157,1765],{},[35,3159,1768],{},[35,3161],{},[22,3163,3164,3168,3170],{},[35,3165,3166],{},[38,3167,1777],{},[35,3169,1780],{},[35,3171],{},[22,3173,3174,3178,3180],{},[35,3175,3176],{},[38,3177,1789],{},[35,3179,1792],{},[35,3181,3182],{},[38,3183,1797],{},[22,3185,3186,3190,3192],{},[35,3187,3188],{},[38,3189,1804],{},[35,3191,1807],{},[35,3193,1810],{},[22,3195,3196,3200,3202],{},[35,3197,3198],{},[38,3199,1817],{},[35,3201,1820],{},[35,3203],{},[22,3205,3206,3210,3212],{},[35,3207,3208],{},[38,3209,1829],{},[35,3211,1832],{},[35,3213],{},[1836,3215,3216],{},[724,3217,1840,3218,1844],{},[38,3219,1843],{},[1720,3221],{},[115,3223,1850],{"id":1849},[198,3225,1854],{"id":1853},[724,3227,1857,3228,1861],{},[38,3229,1860],{},[724,3231,3232,1867,3234,1871],{},[38,3233,1866],{},[38,3235,1870],{},[724,3237,3238],{},[38,3239,1876],{},[120,3241,3242,3244,3246,3248],{},[123,3243,1881],{},[123,3245,1884],{},[123,3247,1887],{},[123,3249,1890],{},[724,3251,3252],{},[38,3253,1895],{},[120,3255,3256,3260,3264,3268,3272],{},[123,3257,3258,1903],{},[38,3259,1902],{},[123,3261,3262,1909],{},[38,3263,1908],{},[123,3265,3266,1915],{},[38,3267,1914],{},[123,3269,3270,1921],{},[38,3271,1920],{},[123,3273,3274,1927],{},[38,3275,1926],{},[724,3277,3278],{},[38,3279,1932],{},[152,3281,3282,3284,3286],{},[123,3283,1937],{},[123,3285,1940],{},[123,3287,1943],{},[1720,3289],{},[198,3291,1949],{"id":1948},[724,3293,3294,1955],{},[38,3295,1954],{},[1957,3297,1960],{"id":1959},[724,3299,3300,1966],{},[38,3301,1965],{},[724,3303,3304],{},[38,3305,1971],{},[152,3307,3308,3312,3316,3320],{},[123,3309,3310,1979],{},[38,3311,1978],{},[123,3313,3314,1985],{},[38,3315,1984],{},[123,3317,3318,1991],{},[38,3319,1990],{},[123,3321,3322,1997],{},[38,3323,1996],{},[1836,3325,3326],{},[724,3327,2002],{},[724,3329,3330],{},[38,3331,2007],{},[120,3333,3334,3338,3342,3346],{},[123,3335,3336,2015],{},[38,3337,2014],{},[123,3339,3340,2021],{},[38,3341,2020],{},[123,3343,3344,2027],{},[38,3345,2026],{},[123,3347,3348,2033,3350,2037],{},[38,3349,2032],{},[38,3351,2036],{},[1957,3353,2041],{"id":2040},[724,3355,2044,3356,2048],{},[38,3357,2047],{},[724,3359,3360],{},[38,3361,2053],{},[120,3363,3364,3368],{},[123,3365,3366,2061],{},[38,3367,2060],{},[123,3369,3370,2067],{},[38,3371,2066],{},[724,3373,3374],{},[38,3375,2072],{},[120,3377,3378,3382,3386],{},[123,3379,3380,2080],{},[38,3381,2079],{},[123,3383,3384,2086],{},[38,3385,2085],{},[123,3387,3388,2092],{},[38,3389,2091],{},[724,3391,3392,2098],{},[38,3393,2097],{},[1720,3395],{},[198,3397,2104],{"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algoritmy jsou rodina optimalizačních metod inspirovaných přírodními procesy — evolucí, chováním rojů, imunitním systémem aj. Umožňují řešit složité optimalizační úlohy, kde klasické gradientní metody selhávají. Každý algoritmus má své klady a zápory — je nutné prozkoumat, který bude aplikaci nejlépe vyhovovat.",[724,3942,1645,3943,3947,3948,1343,3951,1661],{},[207,3944,3946],{"className":3945,"dataFsResolvedFilePath":1282,"href":1283},[210],"genetické algoritmy"," (podmnožina EA), ",[207,3949,1619],{"className":3950,"dataFsResolvedFilePath":1398,"href":1399},[210],[207,3952,1620],{"className":3953,"dataFsResolvedFilePath":1303,"href":1304},[210],[115,3955,3957],{"id":3956},"základní-princip","Základní princip",[120,3959,3960,3970,3973],{},[123,3961,3962,3963,3966,3967],{},"Hledáme optimum ",[38,3964,3965],{},"účelové funkce"," za daných ",[38,3968,3969],{},"omezujících podmínek",[123,3971,3972],{},"Algoritmy pracují iterativně s kandidátními řešeními",[123,3974,3975],{},"Parametry výpočtu: velikost populace, počet iterací, specifické parametry algoritmu",[115,3977,3979],{"id":3978},"ga-vs-ea-hierarchie","GA vs. EA — hierarchie",[724,3981,3982,3985],{},[38,3983,3984],{},"Evoluční algoritmy (EA)"," jsou zastřešující pojem. Zahrnují:",[120,3987,3988,3999,4005,4011],{},[123,3989,3990,3993,3994,3998],{},[38,3991,3992],{},"Genetické algoritmy (GA)"," — binární kódování, selekce, crossover, mutace (",[207,3995,3997],{"className":3996,"dataFsResolvedFilePath":1282,"href":1283},[210],"viz téma",")",[123,4000,4001,4004],{},[38,4002,4003],{},"Evoluční strategie (ES)"," — reálné vektory, důraz na mutaci",[123,4006,4007,4010],{},[38,4008,4009],{},"Diferenciální evoluce (DE)"," — mutace jako rozdíl vektorů",[123,4012,4013,4016],{},[38,4014,4015],{},"Genetické programování (GP)"," — jedinci jsou programy\u002Fstromy",[724,4018,4019,4022],{},[38,4020,4021],{},"Klíčový rozdíl:"," GA je podmnožinou EA. GA je definován specifickými operátory (zejména crossover) a typicky binárním kódováním.",[1720,4024],{},[115,4026,4028],{"id":4027},"trajektoriové-metaheuristiky","Trajektoriové metaheuristiky",[198,4030,4032],{"id":4031},"hill-climbing-výstup-na-kopec","Hill Climbing (Výstup na kopec)",[724,4034,4035],{},"Jednoduché lokální prohledávání — iterativně přechází do lepšího sousedního řešení.",[724,4037,4038],{},[38,4039,4040],{},"Varianty:",[120,4042,4043,4049,4055,4061],{},[123,4044,4045,4048],{},[38,4046,4047],{},"Steepest Ascent"," — vyhodnotí všechny sousedy, vybere nejlepšího",[123,4050,4051,4054],{},[38,4052,4053],{},"First-Choice"," — přijme prvního lepšího souseda (rychlejší)",[123,4056,4057,4060],{},[38,4058,4059],{},"Stochastic"," — náhodně vybírá z lepších sousedů",[123,4062,4063,4066],{},[38,4064,4065],{},"Random Restart"," — opakovaně spouští HC z náhodných startů → překonává lokální optima",[724,4068,4069,4072],{},[38,4070,4071],{},"Problém:"," Uvízne v lokálním optimu — nemá mechanismus pro přijetí horšího řešení.",[1720,4074],{},[198,4076,4078],{"id":4077},"simulated-annealing-simulované-žíhání","Simulated Annealing (Simulované žíhání)",[724,4080,4081],{},"Pravděpodobnostní metaheuristika inspirovaná metalurgickým žíháním kovů.",[724,4083,4084],{},[38,4085,4086],{},"Klíčové pojmy:",[120,4088,4089,4095,4105],{},[123,4090,4091,4094],{},[38,4092,4093],{},"Teplota T"," — řídí míru ochoty přijmout horší řešení. Vysoká T ≈ velká pravděpodobnost; T → 0 ≈ přijímáme jen lepší.",[123,4096,4097,4100,4101,4104],{},[38,4098,4099],{},"Cooling schedule"," — geometrické chlazení: ",[1740,4102,4103],{},"T := α · T",", kde α ∈ (0,8; 0,995). Příliš rychlé → lokální optimum; příliš pomalé → algoritmus běží velmi dlouho.",[123,4106,4107,4110],{},[38,4108,4109],{},"Metropolisovo kritérium"," — horší řešení (ΔE > 0) přijmeme s pravděpodobností:",[1733,4112,4115],{"className":4113,"code":4114,"language":1738},[1736],"P = exp(-ΔE \u002F T)\n",[1740,4116,4114],{"__ignoreMap":641},[724,4118,4119],{},[38,4120,4121],{},"Pseudokód:",[1733,4123,4126],{"className":4124,"code":4125,"language":1738},[1736],"s ← náhodné počáteční řešení\nT ← T_max\n\nopakuj dokud T > T_min:\n    s_new ← náhodný soused(s)\n    ΔE ← E(s_new) - E(s)\n\n    pokud ΔE \u003C 0:\n        s ← s_new               \u002F\u002F lepší řešení vždy přijmeme\n    jinak:\n        pokud random(0,1) \u003C exp(-ΔE \u002F T):\n            s ← s_new           \u002F\u002F horší řešení přijmeme s pravděp. P\n\n    T ← α · T                   \u002F\u002F geometrické ochlazování\n\nvrať s\n",[1740,4127,4125],{"__ignoreMap":641},[724,4129,4130,4132],{},[38,4131,1895],{}," PCB optimalizace, TSP, rozvrhování.",[1720,4134],{},[198,4136,4138],{"id":4137},"tabu-search-prohledávání-se-zákazem","Tabu Search (Prohledávání se zákazem)",[724,4140,4141],{},"Metaheuristika pro kombinatorickou optimalizaci (Fred Glover, 1986\u002F1989). Používá paměť pro systematický průzkum stavového prostoru.",[724,4143,4144],{},[38,4145,4086],{},[120,4147,4148,4154,4160],{},[123,4149,4150,4153],{},[38,4151,4152],{},"Tabu list"," — seznam nedávno provedených tahů. Tahy na seznamu jsou zakázány → brání cyklení. Pevná velikost, nejstarší záznamy se odstraňují.",[123,4155,4156,4159],{},[38,4157,4158],{},"Aspirační kritérium"," — výjimka ze zákazu: pokud tabu tah vede k řešení lepšímu než dosud nejlepší, zákaz se ignoruje.",[123,4161,4162,4165],{},[38,4163,4164],{},"Dlouhodobá paměť"," — sleduje frekventovaně navštívené oblasti; přesměruje prohledávání do neprozkoumaných oblastí (diverzifikace).",[724,4167,4168],{},[38,4169,4121],{},[1733,4171,4174],{"className":4172,"code":4173,"language":1738},[1736],"s ← počáteční řešení\ns_best ← s\ntabu_list ← prázdný\n\nopakuj dokud podmínka ukončení:\n    N ← vygeneruj sousední řešení\n    admissible ← { s' ∈ N | s' není tabu NEBO splňuje aspirační kritérium }\n    s ← nejlepší z admissible\n\n    pokud E(s) \u003C E(s_best):\n        s_best ← s\n\n    aktualizuj tabu_list\n\nvrať s_best\n",[1740,4175,4173],{"__ignoreMap":641},[724,4177,4178,4180],{},[38,4179,1895],{}," Rozvrhování (job scheduling), TSP, optimalizace sítí.",[1720,4182],{},[115,4184,4186],{"id":4185},"rojové-metody-swarm-intelligence","Rojové metody (Swarm Intelligence)",[198,4188,4190],{"id":4189},"ant-colony-optimization-aco","Ant Colony Optimization (ACO)",[724,4192,4193],{},"Inspirováno mravenci hledajícími cestu k potravě. Kratší cesty jsou více frekventovány → více feromonu → pozitivní zpětná vazba.",[724,4195,4196],{},[38,4197,4086],{},[120,4199,4200,4206,4216],{},[123,4201,4202,4205],{},[38,4203,4204],{},"Feromonová stopa τ_xy"," — míra atraktivity hrany. Vyšší = větší pravděpodobnost výběru.",[123,4207,4208,4211,4212,4215],{},[38,4209,4210],{},"Evaporace"," — ",[1740,4213,4214],{},"τ_xy := (1 − ρ) · τ_xy + Σ Δτ_xy^k",". Bez evaporace by algoritmus rychle konvergoval k první nalezené (suboptimální) cestě.",[123,4217,4218,4221,4222,4225],{},[38,4219,4220],{},"Heuristická informace η_xy"," — typicky ",[1740,4223,4224],{},"η = 1\u002Fd_xy"," (inverze vzdálenosti).",[724,4227,4228],{},[38,4229,4230],{},"Pravděpodobnostní vzorec výběru uzlu:",[1733,4232,4235],{"className":4233,"code":4234,"language":1738},[1736],"p_xy^k = (τ_xy^α · η_xy^β) \u002F Σ_z (τ_xz^α · η_xz^β)\n",[1740,4236,4234],{"__ignoreMap":641},[724,4238,4239],{},"kde α = váha feromonu, β = váha heuristiky.",[724,4241,4242,4244],{},[38,4243,1895],{}," TSP, optimalizace sítí, logistika.",[1720,4246],{},[198,4248,4250],{"id":4249},"particle-swarm-optimization-pso","Particle Swarm Optimization (PSO)",[724,4252,4253],{},"Simuluje chování ptačího hejna nebo rybí líhně (Kennedy a Eberhart, 1995).",[724,4255,4256],{},[38,4257,4086],{},[120,4259,4260,4266,4272,4278,4284],{},[123,4261,4262,4265],{},[38,4263,4264],{},"pbest"," — nejlepší pozice, kterou daná částice dosud navštívila",[123,4267,4268,4271],{},[38,4269,4270],{},"gbest"," — nejlepší pozice celého hejna",[123,4273,4274,4277],{},[38,4275,4276],{},"w"," (inertia weight) — setrvačnost: vysoké w = explorace, nízké w = exploatace",[123,4279,4280,4283],{},[38,4281,4282],{},"c1"," (kognitivní koeficient) — přitažlivost k vlastnímu pbest",[123,4285,4286,4289],{},[38,4287,4288],{},"c2"," (sociální koeficient) — přitažlivost ke gbest",[724,4291,4292],{},[38,4293,4294],{},"Vzorec pro aktualizaci rychlosti a polohy:",[1733,4296,4299],{"className":4297,"code":4298,"language":1738},[1736],"v_i,d ← w · v_i,d + c1 · r1 · (pbest_i,d - x_i,d) + c2 · r2 · (gbest_d - x_i,d)\nx_i,d ← x_i,d + v_i,d\n",[1740,4300,4298],{"__ignoreMap":641},[724,4302,4303,4304,1661],{},"kde r1, r2 jsou náhodná čísla z ",[883,4305,4306],{},"0, 1",[724,4308,4309,4311,4312,4315],{},[38,4310,1895],{}," Spojitá optimalizace, trénování ",[207,4313,2966],{"className":4314,"dataFsResolvedFilePath":1268,"href":1269},[210],", optimalizace parametrů.",[1720,4317],{},[198,4319,4321],{"id":4320},"soma-self-organizing-migrating-algorithm","SOMA — Self-Organizing Migrating Algorithm",[724,4323,4324],{},"Česká metaheuristika (Ivan Zelinka, VŠB Ostrava). Jedinci migrují k nejlepšímu jedinci (Leaderovi), místo reprodukce.",[724,4326,4327],{},[38,4328,4086],{},[120,4330,4331,4337,4343,4349],{},[123,4332,4333,4336],{},[38,4334,4335],{},"Leader"," — jedinec s nejlepší hodnotou účelové funkce v populaci (přehodnocuje se každou migraci)",[123,4338,4339,4342],{},[38,4340,4341],{},"PathLength"," — jak daleko za Leadera jedinec „přestřelí\" (typicky 3,0)",[123,4344,4345,4348],{},[38,4346,4347],{},"Step"," — velikost kroku; menší = jemnější prohledávání trasy, více vyhodnocení funkce",[123,4350,4351,4354],{},[38,4352,4353],{},"PRT vektor"," — perturbační vektor: každá dimenze pohybu je s pravděpodobností (1−PRT) „zmrazena\" → diverzita",[724,4356,4357],{},[38,4358,4359],{},"Strategie AllToOne — pseudokód:",[1733,4361,4364],{"className":4362,"code":4363,"language":1738},[1736],"urči Leader ← nejlepší f(x) v populaci\n\npro každého jedince x_i ≠ Leader:\n    t ← 0\n    x_i_best ← x_i\n\n    opakuj dokud t \u003C PathLength:\n        vygeneruj PRT vektor (dim = 1 s pravděp. PRT, jinak 0)\n        x_trial = x_i + t · (Leader - x_i) · PRT_vektor\n\n        pokud f(x_trial) \u003C f(x_i_best):\n            x_i_best ← x_trial\n\n        t ← t + Step\n\n    x_i ← x_i_best    \u002F\u002F přesuň jedince na nejlepší pozici na trase\n\naktualizuj Leader pro příští migraci\n",[1740,4365,4363],{"__ignoreMap":641},[1720,4367],{},[198,4369,4371],{"id":4370},"artificial-bee-colony-abc","Artificial Bee Colony (ABC)",[724,4373,4374],{},"Inspirováno chováním včelího roje (Derviş Karaboğa, 2005).",[724,4376,4377],{},[38,4378,4379],{},"Tři typy včel:",[120,4381,4382,4388,4394],{},[123,4383,4384,4387],{},[38,4385,4386],{},"Employed bees"," (zaměstnané) — přiřazeny ke zdroji, prohledávají okolí, sdílejí informace",[123,4389,4390,4393],{},[38,4391,4392],{},"Onlooker bees"," (čekající) — vybírají zdroj pravděpodobnostně podle kvality (waggle dance), ruletová selekce",[123,4395,4396,4399],{},[38,4397,4398],{},"Scout bees"," (průzkumné) — po vyčerpání zdroje hledají náhodně nový → udržují diverzitu",[1720,4401],{},[198,4403,4405],{"id":4404},"glowworm-swarm-optimization-gso","Glowworm Swarm Optimization (GSO)",[724,4407,4408],{},"Inspirováno světluškami (Krishnanand a Ghose, 2005).",[724,4410,4411,4413,4414,1661],{},[38,4412,1866],{}," Luciferin odpovídá kvalitě řešení. Světluška se pohybuje k jasnějšímu (lepšímu) sousedovi. Přirozeně nachází více optim naráz — vhodné pro ",[38,4415,4416],{},"multimodální optimalizaci",[724,4418,4419,2259,4422],{},[38,4420,4421],{},"Aktualizace luceferinu:",[1740,4423,4424],{},"l_i ← (1 − ρ) · l_i + γ · J(x_i)",[1720,4426],{},[115,4428,4430],{"id":4429},"evoluční-algoritmy-detailní","Evoluční algoritmy (detailní)",[198,4432,4434],{"id":4433},"differential-evolution-de","Differential Evolution (DE)",[724,4436,4437],{},"Evoluční algoritmus pro spojitou optimalizaci (Storn a Price, 1997). Mutace jako rozdíl vektorů — nevyžaduje gradient.",[724,4439,4440],{},[38,4441,4442],{},"Klíčové parametry:",[120,4444,4445,4454],{},[123,4446,4447,4450,4451],{},[38,4448,4449],{},"F"," (scaling factor) — váha diferenčního vektoru, typicky F ≈ 0,8; F ∈ ",[883,4452,4453],{},"0, 2",[123,4455,4456,4459,4460],{},[38,4457,4458],{},"CR"," (crossover rate) — pravděpodobnost přijetí hodnoty z mutantu, typicky CR ≈ 0,9; CR ∈ ",[883,4461,4306],{},[724,4463,4464],{},[38,4465,4466],{},"Vzorec mutace (strategie DE\u002Frand\u002F1):",[1733,4468,4471],{"className":4469,"code":4470,"language":1738},[1736],"y_i = x_a + F · (x_b - x_c)\n",[1740,4472,4470],{"__ignoreMap":641},[724,4474,4475],{},"kde a, b, c jsou tři náhodně vybraní jedinci (a ≠ b ≠ c ≠ i).",[724,4477,4478],{},[38,4479,4480],{},"Jedna generace (pseudokód):",[1733,4482,4485],{"className":4483,"code":4484,"language":1738},[1736],"pro každého jedince x_i:\n    \u002F\u002F Mutace\n    y_i = x_a + F · (x_b - x_c)\n\n    \u002F\u002F Křížení (binomiální)\n    pro každou dimenzi d:\n        pokud random(0,1) \u003C CR nebo d = d_rand:\n            trial_i,d = y_i,d      \u002F\u002F z mutantu\n        jinak:\n            trial_i,d = x_i,d     \u002F\u002F z originálu\n\n    \u002F\u002F Selekce (greedy)\n    pokud f(trial_i) ≤ f(x_i):\n        x_i ← trial_i\n",[1740,4486,4484],{"__ignoreMap":641},[1720,4488],{},[198,4490,4492],{"id":4491},"artificial-immune-system-ais-clonalg","Artificial Immune System (AIS) — CLONALG",[724,4494,4495],{},"Inspirováno biologickým imunitním systémem (De Castro a Von Zuben, 2000).",[724,4497,4498],{},[38,4499,4086],{},[120,4501,4502,4508,4514,4520,4526,4532],{},[123,4503,4504,4507],{},[38,4505,4506],{},"Antigen"," — optimalizační problém",[123,4509,4510,4513],{},[38,4511,4512],{},"Protilátka"," — kandidátní řešení",[123,4515,4516,4519],{},[38,4517,4518],{},"Afinita"," — míra kvality řešení",[123,4521,4522,4525],{},[38,4523,4524],{},"Klonální selekce"," — jedinci s vyšší afinitou vytvářejí více klonů",[123,4527,4528,4531],{},[38,4529,4530],{},"Hypermutace"," — intenzita mutace ∝ 1\u002Fafinita (slabší jedinci mutují silněji)",[123,4533,4534,4537],{},[38,4535,4536],{},"Paměťové buňky"," — uchovávají nejlepší nalezená řešení",[724,4539,4540],{},[38,4541,4542],{},"Pseudokód (CLONALG):",[1733,4544,4547],{"className":4545,"code":4546,"language":1738},[1736],"inicializuj populaci P náhodně; inicializuj paměť M\n\nopakuj dokud podmínka ukončení:\n    vypočti afinitu f(p_i) pro každého jedince\n    vyber n nejlepších protilátek\n    klonuj je (počet klonů ∝ afinita)\n    aplikuj hypermutaci (intenzita ∝ 1\u002Fafinita)\n    vyber nejlepší klony → aktualizuj M\n    nahraď nejhorší jedince náhodnými novými\n\nvrať nejlepší z M\n",[1740,4548,4546],{"__ignoreMap":641},[1720,4550],{},[115,4552,4554],{"id":4553},"základní-prohledávací-metody","Základní prohledávací metody",[16,4556,4557,4569],{},[19,4558,4559],{},[22,4560,4561,4564,4566],{},[25,4562,4563],{},"Metoda",[25,4565,2875],{},[25,4567,4568],{},"Kdy použít",[30,4570,4571,4584,4597,4610,4623,4636],{},[22,4572,4573,4578,4581],{},[35,4574,4575],{},[38,4576,4577],{},"Exhaustive Search",[35,4579,4580],{},"Prohledá úplně všechna řešení; garantuje optimum",[35,4582,4583],{},"Malé prostory (do ~10⁶ kombinací)",[22,4585,4586,4591,4594],{},[35,4587,4588],{},[38,4589,4590],{},"Random Search",[35,4592,4593],{},"Náhodné vzorkování; vrací nejlepší nalezené",[35,4595,4596],{},"Baseline, extrémně nespojité prostory",[22,4598,4599,4604,4607],{},[35,4600,4601],{},[38,4602,4603],{},"Blind Search",[35,4605,4606],{},"Bez heuristické informace (BFS, DFS, random)",[35,4608,4609],{},"Neinformované prohledávání",[22,4611,4612,4617,4620],{},[35,4613,4614],{},[38,4615,4616],{},"Scatter Search",[35,4618,4619],{},"Kombinace referenčních řešení z různých oblastí",[35,4621,4622],{},"Kombinatorická optimalizace",[22,4624,4625,4630,4633],{},[35,4626,4627],{},[38,4628,4629],{},"Backtracking",[35,4631,4632],{},"Zpětné vracení při neúspěchu",[35,4634,4635],{},"Constraint satisfaction problémy",[22,4637,4638,4643,4646],{},[35,4639,4640],{},[38,4641,4642],{},"Greedy",[35,4644,4645],{},"V každém kroku lokálně nejlepší volba",[35,4647,4648],{},"Funguje pro MST (Kruskal, Prim); selhává pro knapsack, mince",[1720,4650],{},[115,4652,4654],{"id":4653},"přehledová-tabulka-všech-algoritmů","Přehledová tabulka všech algoritmů",[16,4656,4657,4675],{},[19,4658,4659],{},[22,4660,4661,4663,4666,4669,4672],{},[25,4662,2187],{},[25,4664,4665],{},"Typ",[25,4667,4668],{},"Inspirace",[25,4670,4671],{},"Klíčový mechanismus",[25,4673,4674],{},"Vhodné pro",[30,4676,4677,4694,4711,4727,4744,4760,4776,4792,4808,4825,4841],{},[22,4678,4679,4682,4685,4688,4691],{},[35,4680,4681],{},"Hill Climbing",[35,4683,4684],{},"Lokální",[35,4686,4687],{},"—",[35,4689,4690],{},"Iterativní zlepšování",[35,4692,4693],{},"Jednoduché problémy",[22,4695,4696,4699,4702,4705,4708],{},[35,4697,4698],{},"Simulated Annealing",[35,4700,4701],{},"Trajektoriová",[35,4703,4704],{},"Metalurgie",[35,4706,4707],{},"Metropolisovo kritérium, chlazení",[35,4709,4710],{},"Kombinatorická i spojitá",[22,4712,4713,4716,4718,4721,4724],{},[35,4714,4715],{},"Tabu Search",[35,4717,4701],{},[35,4719,4720],{},"Lidská paměť",[35,4722,4723],{},"Tabu list, aspirace",[35,4725,4726],{},"Kombinatorická",[22,4728,4729,4732,4735,4738,4741],{},[35,4730,4731],{},"Genetic Algorithm",[35,4733,4734],{},"Evoluční",[35,4736,4737],{},"Biologie",[35,4739,4740],{},"Selekce, crossover, mutace",[35,4742,4743],{},"Diskrétní i spojité",[22,4745,4746,4749,4751,4754,4757],{},[35,4747,4748],{},"Differential Evolution",[35,4750,4734],{},[35,4752,4753],{},"Evoluce",[35,4755,4756],{},"Mutace rozdílem vektorů",[35,4758,4759],{},"Spojitá optimalizace",[22,4761,4762,4765,4768,4771,4774],{},[35,4763,4764],{},"PSO",[35,4766,4767],{},"Swarm",[35,4769,4770],{},"Ptačí hejna",[35,4772,4773],{},"pbest + gbest + inertia",[35,4775,4759],{},[22,4777,4778,4781,4783,4786,4789],{},[35,4779,4780],{},"ACO",[35,4782,4767],{},[35,4784,4785],{},"Mravenci",[35,4787,4788],{},"Feromony, evaporace",[35,4790,4791],{},"Kombinatorická (grafy)",[22,4793,4794,4797,4799,4802,4805],{},[35,4795,4796],{},"SOMA",[35,4798,4767],{},[35,4800,4801],{},"Sociální chování",[35,4803,4804],{},"Migrace k Leaderovi, PRT",[35,4806,4807],{},"Spojitá i diskrétní",[22,4809,4810,4813,4816,4819,4822],{},[35,4811,4812],{},"AIS (CLONALG)",[35,4814,4815],{},"Imuno",[35,4817,4818],{},"Imunitní systém",[35,4820,4821],{},"Klonální selekce, hypermutace",[35,4823,4824],{},"Optimalizace, pattern rec.",[22,4826,4827,4830,4832,4835,4838],{},[35,4828,4829],{},"Artificial Bee Colony",[35,4831,4767],{},[35,4833,4834],{},"Včely",[35,4836,4837],{},"Employed\u002FOnlooker\u002FScout",[35,4839,4840],{},"Spojitá i kombinatorická",[22,4842,4843,4846,4848,4851,4854],{},[35,4844,4845],{},"Glowworm Swarm",[35,4847,4767],{},[35,4849,4850],{},"Světlušky",[35,4852,4853],{},"Luciferin, pohyb k jasnějšímu",[35,4855,4856],{},"Multimodální optimalizace",[115,4858,1692],{"id":1691},[120,4860,4861,4864,4870,4873,4880],{},[123,4862,4863],{},"Rozvrhování výroby a výuky",[123,4865,4866,4869],{},[207,4867,1400],{"className":4868,"dataFsResolvedFilePath":1398,"href":1399},[210]," ekonomických problémů (min. nákladů, min. rizik)",[123,4871,4872],{},"Optimalizace technických systémů",[123,4874,4875,4876,4879],{},"Trénování ",[207,4877,2966],{"className":4878,"dataFsResolvedFilePath":1268,"href":1269},[210]," a ladění parametrů modelů",[123,4881,4882,4885],{},[207,4883,1305],{"className":4884,"dataFsResolvedFilePath":1303,"href":1304},[210]," — klastrování dat (PSO, ABC)",[115,4887,2732],{"id":2731},[152,4889,4890,4893,4896],{},[123,4891,4892],{},"Popište metodu a vysvětlete princip evolučních algoritmů.",[123,4894,4895],{},"Popište realizaci a výpočet evolučních algoritmů na počítači.",[123,4897,4898],{},"Jak lze využít evolučních algoritmů v praxi?",[115,4900,2765],{"id":2764},[724,4902,4903],{},"Evoluční algoritmy, optimalizace, účelová funkce, omezující podmínky, parametry výpočtu, Exhaustive Search, Random Search, Blind Search, Scatter Search, Backtracking, Greedy, Hill Climbing, Tabu Search, Simulated Annealing, Ant Colony, Particle Swarms, Artificial Bee Colony, Glowworm Swarm, Genetic Search, DNA Based Genetic Algorithm, Parallel Genetic Search, Diploid and Haploid Genetic Search, Differential Evolution, Artificial Immune System, SOMA Evolution Strategy, Psychoclonal Search.",[115,4905,2772,4906],{"id":2771},[207,4907,1176],{"className":4908,"dataFsResolvedFilePath":2776,"href":2777},[210],[120,4910,4911,4917],{},[123,4912,4913,4916],{},[207,4914,2785],{"className":4915,"dataFsResolvedFilePath":1562,"href":1563},[210]," — přehled algoritmů, kontrolní otázky, pojmy k zapamatování",[123,4918,4919,4923],{},[207,4920,4922],{"className":4921,"dataFsResolvedFilePath":1571,"href":1572},[210],"Principy a přehled"," — pseudokódy, vzorce, detailní principy (Wikipedia, Cornell, Springer)",{"title":641,"searchDepth":642,"depth":642,"links":4925},[4926,4927,4928,4933,4940,4944,4945,4946,4947,4948,4949],{"id":3956,"depth":642,"text":3957},{"id":3978,"depth":642,"text":3979},{"id":4027,"depth":642,"text":4028,"children":4929},[4930,4931,4932],{"id":4031,"depth":649,"text":4032},{"id":4077,"depth":649,"text":4078},{"id":4137,"depth":649,"text":4138},{"id":4185,"depth":642,"text":4186,"children":4934},[4935,4936,4937,4938,4939],{"id":4189,"depth":649,"text":4190},{"id":4249,"depth":649,"text":4250},{"id":4320,"depth":649,"text":4321},{"id":4370,"depth":649,"text":4371},{"id":4404,"depth":649,"text":4405},{"id":4429,"depth":642,"text":4430,"children":4941},[4942,4943],{"id":4433,"depth":649,"text":4434},{"id":4491,"depth":649,"text":4492},{"id":4553,"depth":642,"text":4554},{"id":4653,"depth":642,"text":4654},{"id":1691,"depth":642,"text":1692},{"id":2731,"depth":642,"text":2732},{"id":2764,"depth":642,"text":2765},{"id":2771,"depth":642,"text":2821},{},"\u002Ftopics\u002Fevolucni-algoritmy",{"title":1385,"description":3940},[1608,1609],"topics\u002Fevolucni-algoritmy",[1601,1617,4956,4957,4958,4959,4960,4961],"metaheuristiky","simulated-annealing","tabu-search","aco","pso","soma","2iZO9GpjkAfcGdCCz6z2lyz5UKhCMs6jY6tqmgvxlhQ",{"id":4964,"title":1249,"body":4965,"course":659,"courses":5183,"created":1602,"description":641,"extension":661,"meta":5184,"navigation":664,"path":5185,"seo":5186,"sources":5187,"stem":5190,"tags":5191,"type":2835,"updated":677,"__hash__":5196},"topics\u002Ftopics\u002Ffuzzy-logika.md",{"type":9,"value":4966,"toc":5173},[4967,4969,4975,4982,4986,5012,5016,5048,5051,5055,5069,5073,5090,5094,5118,5120,5143,5145,5148,5153],[12,4968,1249],{"id":1649},[724,4970,4971],{},[2853,4972],{"alt":1649,"className":4973,"src":4974},[210,2857],"\u002Fwiki-assets\u002Ffuzzy-logika.jpeg",[724,4976,4977,4978,4981],{},"Metoda modelování rozhodování s vágními (neostrými) pojmy. Na rozdíl od klasické binární logiky (0\u002F1) pracuje fuzzy logika s ",[38,4979,4980],{},"mírou členství"," μ ∈ ⟨0, 1⟩ — prvek může patřit do více množin současně s různou intenzitou.",[115,4983,4985],{"id":4984},"základní-principy","Základní principy",[120,4987,4988,4994,5000,5006],{},[123,4989,4990,4993],{},[38,4991,4992],{},"Funkce členství"," — přiřazuje každému prvku stupeň příslušnosti k fuzzy množině. Základní tvary: L-funkce, trojúhelníková (Λ), trapezoidní (Π), S-funkce, Z-funkce.",[123,4995,4996,4999],{},[38,4997,4998],{},"Jazykové proměnné"," — vágní pojmy (nízké riziko, vysoký plat) formalizované jako termy. Např. riziko: {velmi nízké, nízké, střední, vysoké, velmi vysoké}.",[123,5001,5002,5005],{},[38,5003,5004],{},"Pravidla KDYŽ–POTOM"," — jádro fuzzy inferenčního systému. Modelují expertní znalost. AND = minimum\u002Fsoučin, OR = maximum.",[123,5007,5008,5011],{},[38,5009,5010],{},"Defuzzifikace"," — převod fuzzy výsledku na konečné rozhodnutí (např. normalizace na 0–100 % a rozdělení do kategorií).",[115,5013,5015],{"id":5014},"architektura-fuzzy-systému","Architektura fuzzy systému",[152,5017,5018,5024,5030,5036,5042],{},[123,5019,5020,5023],{},[38,5021,5022],{},"Vstupy"," — číselné veličiny",[123,5025,5026,5029],{},[38,5027,5028],{},"Fuzzifikace"," — převod na stupně členství",[123,5031,5032,5035],{},[38,5033,5034],{},"Blok pravidel"," — KDYŽ–POTOM pravidla",[123,5037,5038,5041],{},[38,5039,5040],{},"Inference"," — vyhodnocení pravidel",[123,5043,5044,5047],{},[38,5045,5046],{},"Výstup"," — fuzzy nebo defuzzifikovaný výsledek",[724,5049,5050],{},"Systém může mít více vstupů i více výstupů (např. celkové riziko + typ investora).",[115,5052,5054],{"id":5053},"nástroje","Nástroje",[120,5056,5057,5063],{},[123,5058,5059,5062],{},[38,5060,5061],{},"Excel"," — jednoduché modely, matice příslušnosti, funkce KDYŽ pro defuzzifikaci",[123,5064,5065,5068],{},[38,5066,5067],{},"MATLAB Fuzzy Logic Toolbox"," — pokročilejší modely, vizualizace, ladění pravidel",[115,5070,5072],{"id":5071},"typické-aplikace","Typické aplikace",[120,5074,5075,5078,5081,5084,5087],{},[123,5076,5077],{},"Hodnocení investičního rizika",[123,5079,5080],{},"Úvěrové skórování",[123,5082,5083],{},"Výběr projektu, hodnocení dodavatele",[123,5085,5086],{},"Rozhodování o výrobě",[123,5088,5089],{},"Profilace investora (averze vs. vyhledávání rizika)",[115,5091,5093],{"id":5092},"propojení-s-dalšími-tématy","Propojení s dalšími tématy",[120,5095,5096,5106,5112],{},[123,5097,5098,5101,5102],{},[207,5099,1415],{"className":5100,"dataFsResolvedFilePath":1413,"href":1414},[210]," — hybridní systém propojující fuzzy logiku s ",[207,5103,5105],{"className":5104,"dataFsResolvedFilePath":1268,"href":1269},[210],"neuronovými sítěmi",[123,5107,5108,5111],{},[207,5109,1297],{"className":5110,"dataFsResolvedFilePath":1295,"href":1296},[210]," — oba přístupy řeší nejistotu, ale jiným způsobem",[123,5113,5114,5117],{},[207,5115,1313],{"className":5116,"dataFsResolvedFilePath":1311,"href":1312},[210]," — fuzzy systémy mohou sloužit jako základ predikčních modelů",[115,5119,2732],{"id":2731},[152,5121,5122,5125,5128,5131,5134,5137,5140],{},[123,5123,5124],{},"Popište metodu a vysvětlete princip fuzzy logiky.",[123,5126,5127],{},"Popište realizaci a výpočet fuzzy logiky na počítači.",[123,5129,5130],{},"Jak lze využít fuzzy logiky v praxi?",[123,5132,5133],{},"Kdo byl zakladatelem fuzzy logiky?",[123,5135,5136],{},"Jaká je posloupnost kroků při zpracování případů fuzzy logikou?",[123,5138,5139],{},"Co znamená proces fuzzifikace?",[123,5141,5142],{},"Co je to defuzzifikace?",[115,5144,2765],{"id":2764},[724,5146,5147],{},"Fuzzy logika, fuzzifikace, fuzzy inference, defuzzifikace, transformační a retransformační matice, vstup, rozhodovací blok, výstup.",[115,5149,2772,5150],{"id":2771},[207,5151,1176],{"className":5152,"dataFsResolvedFilePath":2776,"href":2777},[210],[120,5154,5155,5161,5167],{},[123,5156,5157,5160],{},[207,5158,1493],{"className":5159,"dataFsResolvedFilePath":1491,"href":1492},[210]," — základní princip, funkce členství, implementace",[123,5162,5163,5166],{},[207,5164,1502],{"className":5165,"dataFsResolvedFilePath":1500,"href":1501},[210]," — architektura systému, návrh modelu",[123,5168,5169,5172],{},[207,5170,2785],{"className":5171,"dataFsResolvedFilePath":1562,"href":1563},[210]," — shrnutí kapitoly, kontrolní otázky, pojmy",{"title":641,"searchDepth":642,"depth":642,"links":5174},[5175,5176,5177,5178,5179,5180,5181,5182],{"id":4984,"depth":642,"text":4985},{"id":5014,"depth":642,"text":5015},{"id":5053,"depth":642,"text":5054},{"id":5071,"depth":642,"text":5072},{"id":5092,"depth":642,"text":5093},{"id":2731,"depth":642,"text":2732},{"id":2764,"depth":642,"text":2765},{"id":2771,"depth":642,"text":2821},[1601],{},"\u002Ftopics\u002Ffuzzy-logika",{"title":1249,"description":641},[5188,5189,1608],"raw\u002Fipmrk\u002Ffuzzy-excel.md","raw\u002Fipmrk\u002Ffuzzy-matlab.md","topics\u002Ffuzzy-logika",[1601,1614,5192,5193,5194,5195],"funkce-clenstvi","pravidla","inference","defuzzifikace","2QGb9et6Ck5AGYFKMs7BnN3IeorbBz8DsZp0aSyXVZk",{"id":5198,"title":1284,"body":5199,"course":659,"courses":5523,"created":1602,"description":641,"extension":661,"meta":5524,"navigation":664,"path":5525,"seo":5526,"sources":5527,"stem":5530,"tags":5531,"type":2835,"updated":677,"__hash__":5535},"topics\u002Ftopics\u002Fgeneticke-algoritmy.md",{"type":9,"value":5200,"toc":5510},[5201,5204,5211,5218,5222,5248,5252,5259,5295,5299,5313,5317,5320,5327,5331,5345,5349,5419,5423,5429,5435,5437,5458,5460,5483,5485,5488,5493],[12,5202,1284],{"id":5203},"genetické-algoritmy",[724,5205,5206],{},[2853,5207],{"alt":5208,"className":5209,"src":5210},"ga-cyklus",[210,2857],"\u002Fwiki-assets\u002Fga-cyklus.jpeg",[724,5212,5213,5214,5217],{},"Evoluční optimalizační metoda inspirovaná biologickou dědičností a přirozeným výběrem (Mendel, Darwin). Místo přímého hledání řešení pracuje s ",[38,5215,5216],{},"populací kandidátních řešení",", která se postupně zlepšuje.",[115,5219,5221],{"id":5220},"základní-pojmy","Základní pojmy",[120,5223,5224,5230,5236,5242],{},[123,5225,5226,5229],{},[38,5227,5228],{},"Chromozom"," — kódované řešení (často binární řetězec, např. 1100)",[123,5231,5232,5235],{},[38,5233,5234],{},"Gen"," — jednotlivý bit chromozomu",[123,5237,5238,5241],{},[38,5239,5240],{},"Fitness funkce"," — účelová funkce hodnotící kvalitu řešení",[123,5243,5244,5247],{},[38,5245,5246],{},"Populace"," — soubor chromozomů v jedné generaci",[115,5249,5251],{"id":5250},"cyklus-algoritmu","Cyklus algoritmu",[724,5253,5254],{},[2853,5255],{"alt":5256,"className":5257,"src":5258},"ga-krizeni-mutace",[210,2857],"\u002Fwiki-assets\u002Fga-krizeni-mutace.jpeg",[152,5260,5261,5266,5271,5277,5283,5289],{},[123,5262,5263,5265],{},[38,5264,1978],{}," — vytvoření počáteční (náhodné) populace",[123,5267,5268,5270],{},[38,5269,1324],{}," — ohodnocení každého chromozomu fitness funkcí",[123,5272,5273,5276],{},[38,5274,5275],{},"Selekce"," — výběr lepších jedinců (lepší = větší šance přežít, ale i horší mohou zůstat pro diverzitu)",[123,5278,5279,5282],{},[38,5280,5281],{},"Křížení"," — kombinace dvou rodičů → potomci s vlastnostmi obou (pravděpodobnost ~0,9)",[123,5284,5285,5288],{},[38,5286,5287],{},"Mutace"," — náhodná změna bitu (0↔1), vzácná (~0,1), zabraňuje zamrznutí populace",[123,5290,5291,5294],{},[38,5292,5293],{},"Ukončení?"," — pokud ne, zpět na krok 2 (nová generace)",[115,5296,5298],{"id":5297},"parametry","Parametry",[120,5300,5301,5304,5307,5310],{},[123,5302,5303],{},"Velikost populace (~1000)",[123,5305,5306],{},"Pravděpodobnost křížení (~0,9)",[123,5308,5309],{},"Pravděpodobnost mutace (~0,1 nebo méně)",[123,5311,5312],{},"Kritéria ukončení: max generací, max čas, populace se nemění",[115,5314,5316],{"id":5315},"binární-kódování","Binární kódování",[724,5318,5319],{},"Chromozom jako binární řetězec → převod na reálnou hodnotu:\nH_D = a₃·2³ + a₂·2² + a₁·2¹ + a₀·2⁰",[724,5321,5322,5323,5326],{},"Mapování na interval ",[883,5324,5325],{},"x_min, x_max"," umožňuje optimalizovat reálné parametry.",[115,5328,5330],{"id":5329},"dva-typy-úloh","Dva typy úloh",[120,5332,5333,5339],{},[123,5334,5335,5338],{},[38,5336,5337],{},"Přímá optimalizace"," — min nákladů, max zisku, min času, min odpadu",[123,5340,5341,5344],{},[38,5342,5343],{},"Parametrická optimalizace modelu"," — nejlepší parametry funkce, nejlepší nastavení predikčního systému",[115,5346,5348],{"id":5347},"aplikace","Aplikace",[16,5350,5351,5361],{},[19,5352,5353],{},[22,5354,5355,5358],{},[25,5356,5357],{},"Oblast",[25,5359,5360],{},"Příklad",[30,5362,5363,5371,5379,5387,5395,5403,5411],{},[22,5364,5365,5368],{},[35,5366,5367],{},"Ekonomika",[35,5369,5370],{},"Minimalizace nákladů, maximalizace zisku",[22,5372,5373,5376],{},[35,5374,5375],{},"Výroba",[35,5377,5378],{},"Minimalizace výrobního času, rozvrhování strojů",[22,5380,5381,5384],{},[35,5382,5383],{},"Logistika",[35,5385,5386],{},"Obchodní cestující (TSP), nejkratší trasa",[22,5388,5389,5392],{},[35,5390,5391],{},"Materiál",[35,5393,5394],{},"Cutting plan — řezání s minimálním odpadem",[22,5396,5397,5400],{},[35,5398,5399],{},"Investice",[35,5401,5402],{},"Knapsack — výběr projektů při omezeném rozpočtu",[22,5404,5405,5408],{},[35,5406,5407],{},"Data",[35,5409,5410],{},"Aproximace měřených dat, klastrování, segmentace",[22,5412,5413,5416],{},[35,5414,5415],{},"Finance",[35,5417,5418],{},"[[predikce",[115,5420,5422],{"id":5421},"výhody-a-nevýhody","Výhody a nevýhody",[724,5424,5425,5428],{},[38,5426,5427],{},"Výhody",": nepotřebují derivace, pracují s diskrétními i spojitými problémy, zvládají mnoho lokálních extrémů, univerzálně použitelné.",[724,5430,5431,5434],{},[38,5432,5433],{},"Nevýhody",": negarantují globální optimum, výpočetně náročné, výsledek závisí na nastavení parametrů.",[115,5436,5093],{"id":5092},[120,5438,5439,5446,5452],{},[123,5440,5441,5445],{},[207,5442,5444],{"className":5443,"dataFsResolvedFilePath":1268,"href":1269},[210],"Neuronové sítě"," — GA mohou optimalizovat architekturu sítě",[123,5447,5448,5451],{},[207,5449,1313],{"className":5450,"dataFsResolvedFilePath":1311,"href":1312},[210]," — optimalizace predikčních modelů",[123,5453,5454,5457],{},[207,5455,1249],{"className":5456,"dataFsResolvedFilePath":1247,"href":1248},[210]," — GA mohou ladit parametry fuzzy systému",[115,5459,2732],{"id":2731},[152,5461,5462,5465,5468,5471,5474,5477,5480],{},[123,5463,5464],{},"Popište metodu a vysvětlete princip genetických algoritmů.",[123,5466,5467],{},"Popište realizaci a výpočet genetických algoritmů na počítači.",[123,5469,5470],{},"Jak lze využít genetických algoritmů v praxi?",[123,5472,5473],{},"Jaké jsou prvky reprodukce?",[123,5475,5476],{},"Co znamená proces selekce?",[123,5478,5479],{},"Co znamená proces mutace?",[123,5481,5482],{},"Jaká se volí velikost populace?",[115,5484,2765],{"id":2764},[724,5486,5487],{},"Genetické algoritmy, optimalizace, reprodukce, selekce, křížení, mutace, účelová funkce, omezující podmínky, parametry výpočtu.",[115,5489,2772,5490],{"id":2771},[207,5491,1176],{"className":5492,"dataFsResolvedFilePath":2776,"href":2777},[210],[120,5494,5495,5500,5505],{},[123,5496,5497],{},[207,5498,1538],{"className":5499,"dataFsResolvedFilePath":1536,"href":1537},[210],[123,5501,5502],{},[207,5503,1547],{"className":5504,"dataFsResolvedFilePath":1545,"href":1546},[210],[123,5506,5507,5172],{},[207,5508,2785],{"className":5509,"dataFsResolvedFilePath":1562,"href":1563},[210],{"title":641,"searchDepth":642,"depth":642,"links":5511},[5512,5513,5514,5515,5516,5517,5518,5519,5520,5521,5522],{"id":5220,"depth":642,"text":5221},{"id":5250,"depth":642,"text":5251},{"id":5297,"depth":642,"text":5298},{"id":5315,"depth":642,"text":5316},{"id":5329,"depth":642,"text":5330},{"id":5347,"depth":642,"text":5348},{"id":5421,"depth":642,"text":5422},{"id":5092,"depth":642,"text":5093},{"id":2731,"depth":642,"text":2732},{"id":2764,"depth":642,"text":2765},{"id":2771,"depth":642,"text":2821},[1601],{},"\u002Ftopics\u002Fgeneticke-algoritmy",{"title":1284,"description":641},[5528,5529,1608],"raw\u002Fipmrk\u002Fga-teorie.md","raw\u002Fipmrk\u002Fga-vyuziti.md","topics\u002Fgeneticke-algoritmy",[1601,1616,1619,5532,5533,5534],"selekce","krizeni","mutace","EOZsCFN6Xx3jsNFX_SunmlY9UI9b8VubGTEwPCfPmQ8",{"id":5537,"title":5538,"body":5539,"course":659,"courses":7194,"created":1129,"description":7195,"extension":661,"meta":7196,"navigation":664,"path":7197,"seo":7198,"sources":7199,"stem":7200,"tags":7201,"type":2835,"updated":677,"__hash__":7204},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":5540,"toc":7182},[5541,5544,5661,5668,5689,5691,5698,5765,5786,5790,5793,5933,5937,6150,6187,6329,6333,6398,6414,6442,6446,6544,6548,6552,6608,6714,6933,6937,6980,7086,7138,7142],[12,5542,5538],{"id":5543},"lagrangeova-metoda-vázané-extrémy",[724,5545,5546,5547,5579,5580,5617,5618,5621,5622,5653,5654,5660],{},"Hledáme extrém funkce ",[883,5548,5550],{"className":5549},[886],[888,5551,5552],{"xmlns":890},[892,5553,5554,5576],{},[895,5555,5556,5559,5564,5567,5571,5574],{},[898,5557,5558],{},"f",[5560,5561,5563],"mo",{"stretchy":5562},"false","(",[898,5565,5566],{},"x",[5560,5568,5570],{"separator":5569},"true",",",[898,5572,5573],{},"y",[5560,5575,3998],{"stretchy":5562},[902,5577,5578],{"encoding":904},"f(x, y)"," (resp. ",[883,5581,5583],{"className":5582},[886],[888,5584,5585],{"xmlns":890},[892,5586,5587,5614],{},[895,5588,5589,5591,5593,5603,5605,5612],{},[898,5590,900],{},[5560,5592,5563],{"stretchy":5562},[5594,5595,5596,5599],"msub",{},[898,5597,5598],{},"Q",[5600,5601,5602],"mn",{},"1",[5560,5604,5570],{"separator":5569},[5594,5606,5607,5609],{},[898,5608,5598],{},[5600,5610,5611],{},"2",[5560,5613,3998],{"stretchy":5562},[902,5615,5616],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,5619,5620],{},"podmíněný"," rovnicí ",[883,5623,5625],{"className":5624},[886],[888,5626,5627],{"xmlns":890},[892,5628,5629,5650],{},[895,5630,5631,5634,5636,5638,5640,5642,5644,5647],{},[898,5632,5633],{},"g",[5560,5635,5563],{"stretchy":5562},[898,5637,5566],{},[5560,5639,5570],{"separator":5569},[898,5641,5573],{},[5560,5643,3998],{"stretchy":5562},[5560,5645,5646],{},"=",[5600,5648,5649],{},"0",[902,5651,5652],{"encoding":904},"g(x, y) = 0",". V ",[207,5655,5659],{"className":5656,"dataFsResolvedFilePath":5657,"href":5658},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","matematické ekonomii"," se používá pro:",[724,5662,5663],{},[2853,5664],{"alt":5665,"className":5666,"src":5667},"imek-lagrange-tecnost",[210,2857],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,5669,5670,5680,5686],{},[123,5671,5672,5675,5676,3998],{},[38,5673,5674],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,5677,5679],{"className":5678,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,5681,5682,5685],{},[38,5683,5684],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,5687,5688],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,5690,2875],{"id":2874},[724,5692,5693,5694,5697],{},"Definujeme ",[38,5695,5696],{},"Lagrangeovu funkci",":",[724,5699,5700],{},[883,5701,5703],{"className":5702},[886],[888,5704,5705],{"xmlns":890},[892,5706,5707,5762],{},[895,5708,5709,5712,5714,5716,5718,5720,5722,5725,5727,5729,5731,5733,5735,5737,5739,5741,5744,5746,5750,5752,5754,5756,5758,5760],{},[898,5710,5711],{},"L",[5560,5713,5563],{"stretchy":5562},[898,5715,5566],{},[5560,5717,5570],{"separator":5569},[898,5719,5573],{},[5560,5721,5570],{"separator":5569},[898,5723,5724],{},"λ",[5560,5726,3998],{"stretchy":5562},[5560,5728,5646],{},[898,5730,5558],{},[5560,5732,5563],{"stretchy":5562},[898,5734,5566],{},[5560,5736,5570],{"separator":5569},[898,5738,5573],{},[5560,5740,3998],{"stretchy":5562},[5560,5742,5743],{},"+",[898,5745,5724],{},[5747,5748,5749],"mtext",{}," ",[898,5751,5633],{},[5560,5753,5563],{"stretchy":5562},[898,5755,5566],{},[5560,5757,5570],{"separator":5569},[898,5759,5573],{},[5560,5761,3998],{"stretchy":5562},[902,5763,5764],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,5766,5767,5768,5782,5783,1661],{},"kde ",[883,5769,5771],{"className":5770},[886],[888,5772,5773],{"xmlns":890},[892,5774,5775,5779],{},[895,5776,5777],{},[898,5778,5724],{},[902,5780,5781],{"encoding":904},"\\lambda"," je ",[38,5784,5785],{},"Lagrangeův multiplikátor",[115,5787,5789],{"id":5788},"nutná-podmínka","Nutná podmínka",[724,5791,5792],{},"Řešíme soustavu:",[724,5794,5795,5847,5895],{},[883,5796,5798],{"className":5797},[886],[888,5799,5800],{"xmlns":890},[892,5801,5802,5844],{},[895,5803,5804,5816,5818,5826,5828,5830,5832,5840,5842],{},[5805,5806,5807,5809,5811],"msubsup",{},[898,5808,5711],{},[898,5810,5566],{},[5560,5812,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},"normal","0em","′",[5560,5817,5646],{},[5805,5819,5820,5822,5824],{},[898,5821,5558],{},[898,5823,5566],{},[5560,5825,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5560,5827,5743],{},[898,5829,5724],{},[5747,5831,5749],{},[5805,5833,5834,5836,5838],{},[898,5835,5633],{},[898,5837,5566],{},[5560,5839,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5560,5841,5646],{},[5600,5843,5649],{},[902,5845,5846],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,5848,5850],{"className":5849},[886],[888,5851,5852],{"xmlns":890},[892,5853,5854,5892],{},[895,5855,5856,5864,5866,5874,5876,5878,5880,5888,5890],{},[5805,5857,5858,5860,5862],{},[898,5859,5711],{},[898,5861,5573],{},[5560,5863,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5560,5865,5646],{},[5805,5867,5868,5870,5872],{},[898,5869,5558],{},[898,5871,5573],{},[5560,5873,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5560,5875,5743],{},[898,5877,5724],{},[5747,5879,5749],{},[5805,5881,5882,5884,5886],{},[898,5883,5633],{},[898,5885,5573],{},[5560,5887,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5560,5889,5646],{},[5600,5891,5649],{},[902,5893,5894],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,5896,5898],{"className":5897},[886],[888,5899,5900],{"xmlns":890},[892,5901,5902,5930],{},[895,5903,5904,5912,5914,5916,5918,5920,5922,5924,5926,5928],{},[5805,5905,5906,5908,5910],{},[898,5907,5711],{},[898,5909,5724],{},[5560,5911,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5560,5913,5646],{},[898,5915,5633],{},[5560,5917,5563],{"stretchy":5562},[898,5919,5566],{},[5560,5921,5570],{"separator":5569},[898,5923,5573],{},[5560,5925,3998],{"stretchy":5562},[5560,5927,5646],{},[5600,5929,5649],{},[902,5931,5932],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,5934,5936],{"id":5935},"postačující-podmínka","Postačující podmínka",[724,5938,5939],{},[883,5940,5942],{"className":5941},[886],[888,5943,5944],{"xmlns":890},[892,5945,5946,6147],{},[895,5947,5948,5951,5953,5955,5957,5959,5961,5963,5965,5967,5969,5985,5987,5989,6005,6007,6009,6017,6024,6026,6028,6044,6046,6048,6064,6066,6068,6076,6082,6085,6087,6089,6105,6107,6109,6125,6127,6129,6137,6139],{},[898,5949,5950],{},"D",[5560,5952,5563],{"stretchy":5562},[898,5954,5566],{},[5560,5956,5570],{"separator":5569},[898,5958,5573],{},[5560,5960,5570],{"separator":5569},[898,5962,5724],{},[5560,5964,3998],{"stretchy":5562},[5560,5966,5646],{},[5560,5968,5563],{"stretchy":5562},[5805,5970,5971,5973,5979],{},[898,5972,5558],{},[895,5974,5975,5977],{},[898,5976,5566],{},[898,5978,5566],{},[895,5980,5981,5983],{},[5560,5982,5815],{"mathvariant":5813},[5560,5984,5815],{"mathvariant":5813},[5560,5986,5743],{},[898,5988,5724],{},[5805,5990,5991,5993,5999],{},[898,5992,5633],{},[895,5994,5995,5997],{},[898,5996,5566],{},[898,5998,5566],{},[895,6000,6001,6003],{},[5560,6002,5815],{"mathvariant":5813},[5560,6004,5815],{"mathvariant":5813},[5560,6006,3998],{"stretchy":5562},[5560,6008,5563],{"stretchy":5562},[5805,6010,6011,6013,6015],{},[898,6012,5633],{},[898,6014,5573],{},[5560,6016,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[6018,6019,6020,6022],"msup",{},[5560,6021,3998],{"stretchy":5562},[5600,6023,5611],{},[5560,6025,5743],{},[5560,6027,5563],{"stretchy":5562},[5805,6029,6030,6032,6038],{},[898,6031,5558],{},[895,6033,6034,6036],{},[898,6035,5573],{},[898,6037,5573],{},[895,6039,6040,6042],{},[5560,6041,5815],{"mathvariant":5813},[5560,6043,5815],{"mathvariant":5813},[5560,6045,5743],{},[898,6047,5724],{},[5805,6049,6050,6052,6058],{},[898,6051,5633],{},[895,6053,6054,6056],{},[898,6055,5573],{},[898,6057,5573],{},[895,6059,6060,6062],{},[5560,6061,5815],{"mathvariant":5813},[5560,6063,5815],{"mathvariant":5813},[5560,6065,3998],{"stretchy":5562},[5560,6067,5563],{"stretchy":5562},[5805,6069,6070,6072,6074],{},[898,6071,5633],{},[898,6073,5566],{},[5560,6075,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[6018,6077,6078,6080],{},[5560,6079,3998],{"stretchy":5562},[5600,6081,5611],{},[5560,6083,6084],{},"−",[5600,6086,5611],{},[5560,6088,5563],{"stretchy":5562},[5805,6090,6091,6093,6099],{},[898,6092,5558],{},[895,6094,6095,6097],{},[898,6096,5566],{},[898,6098,5573],{},[895,6100,6101,6103],{},[5560,6102,5815],{"mathvariant":5813},[5560,6104,5815],{"mathvariant":5813},[5560,6106,5743],{},[898,6108,5724],{},[5805,6110,6111,6113,6119],{},[898,6112,5633],{},[895,6114,6115,6117],{},[898,6116,5566],{},[898,6118,5573],{},[895,6120,6121,6123],{},[5560,6122,5815],{"mathvariant":5813},[5560,6124,5815],{"mathvariant":5813},[5560,6126,3998],{"stretchy":5562},[5747,6128,5749],{},[5805,6130,6131,6133,6135],{},[898,6132,5633],{},[898,6134,5566],{},[5560,6136,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5747,6138,5749],{},[5805,6140,6141,6143,6145],{},[898,6142,5633],{},[898,6144,5573],{},[5560,6146,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[902,6148,6149],{"encoding":904},"D(x, y, \\lambda) = (f''_{xx} + \\lambda g''_{xx})(g'_y)^2 + (f''_{yy} + \\lambda g''_{yy})(g'_x)^2 - 2(f''_{xy} + \\lambda g''_{xy})\\, g'_x\\, g'_y",[724,6151,6152,6153,6186],{},"Je-li ",[883,6154,6156],{"className":6155},[886],[888,6157,6158],{"xmlns":890},[892,6159,6160,6183],{},[895,6161,6162,6165,6167,6169,6172,6174,6180],{},[5560,6163,6164],{"stretchy":5562},"[",[898,6166,207],{},[5560,6168,5570],{"separator":5569},[898,6170,6171],{},"b",[5560,6173,5570],{"separator":5569},[5594,6175,6176,6178],{},[898,6177,5724],{},[5600,6179,5649],{},[5560,6181,6182],{"stretchy":5562},"]",[902,6184,6185],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,6188,6189,6260],{},[123,6190,6191,6228,6229,6232,6233],{},[883,6192,6194],{"className":6193},[886],[888,6195,6196],{"xmlns":890},[892,6197,6198,6225],{},[895,6199,6200,6202,6204,6206,6208,6210,6212,6218,6220,6223],{},[898,6201,5950],{},[5560,6203,5563],{"stretchy":5562},[898,6205,207],{},[5560,6207,5570],{"separator":5569},[898,6209,6171],{},[5560,6211,5570],{"separator":5569},[5594,6213,6214,6216],{},[898,6215,5724],{},[5600,6217,5649],{},[5560,6219,3998],{"stretchy":5562},[5560,6221,6222],{},"\u003C",[5600,6224,5649],{},[902,6226,6227],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0"," ⇒ ",[38,6230,6231],{},"maximum"," vázané podmínkou ",[883,6234,6236],{"className":6235},[886],[888,6237,6238],{"xmlns":890},[892,6239,6240,6258],{},[895,6241,6242,6244,6246,6248,6250,6252,6254,6256],{},[898,6243,5633],{},[5560,6245,5563],{"stretchy":5562},[898,6247,5566],{},[5560,6249,5570],{"separator":5569},[898,6251,5573],{},[5560,6253,3998],{"stretchy":5562},[5560,6255,5646],{},[5600,6257,5649],{},[902,6259,5652],{"encoding":904},[123,6261,6262,6228,6299,6232,6302],{},[883,6263,6265],{"className":6264},[886],[888,6266,6267],{"xmlns":890},[892,6268,6269,6296],{},[895,6270,6271,6273,6275,6277,6279,6281,6283,6289,6291,6294],{},[898,6272,5950],{},[5560,6274,5563],{"stretchy":5562},[898,6276,207],{},[5560,6278,5570],{"separator":5569},[898,6280,6171],{},[5560,6282,5570],{"separator":5569},[5594,6284,6285,6287],{},[898,6286,5724],{},[5600,6288,5649],{},[5560,6290,3998],{"stretchy":5562},[5560,6292,6293],{},">",[5600,6295,5649],{},[902,6297,6298],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,6300,6301],{},"minimum",[883,6303,6305],{"className":6304},[886],[888,6306,6307],{"xmlns":890},[892,6308,6309,6327],{},[895,6310,6311,6313,6315,6317,6319,6321,6323,6325],{},[898,6312,5633],{},[5560,6314,5563],{"stretchy":5562},[898,6316,5566],{},[5560,6318,5570],{"separator":5569},[898,6320,5573],{},[5560,6322,3998],{"stretchy":5562},[5560,6324,5646],{},[5600,6326,5649],{},[902,6328,5652],{"encoding":904},[115,6330,6332],{"id":6331},"význam-multiplikátoru","Význam multiplikátoru",[724,6334,6335],{},[883,6336,6338],{"className":6337},[886],[888,6339,6340],{"xmlns":890},[892,6341,6342,6395],{},[895,6343,6344,6346,6348,6371,6373],{},[898,6345,5724],{},[5560,6347,5646],{},[6349,6350,6351,6359],"mfrac",{},[5805,6352,6353,6355,6357],{},[898,6354,5558],{},[898,6356,5566],{},[5560,6358,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[895,6360,6361,6363],{},[5560,6362,6084],{},[5805,6364,6365,6367,6369],{},[898,6366,5633],{},[898,6368,5566],{},[5560,6370,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5560,6372,5646],{},[6349,6374,6375,6383],{},[5805,6376,6377,6379,6381],{},[898,6378,5558],{},[898,6380,5573],{},[5560,6382,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[895,6384,6385,6387],{},[5560,6386,6084],{},[5805,6388,6389,6391,6393],{},[898,6390,5633],{},[898,6392,5573],{},[5560,6394,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[902,6396,6397],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,6399,6400,6413],{},[883,6401,6403],{"className":6402},[886],[888,6404,6405],{"xmlns":890},[892,6406,6407,6411],{},[895,6408,6409],{},[898,6410,5724],{},[902,6412,5781],{"encoding":904}," udává:",[120,6415,6416,6422],{},[123,6417,6418,6419],{},"konstantní ",[38,6420,6421],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,6423,6424,6427,6428,6441],{},[38,6425,6426],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,6429,6431],{"className":6430},[886],[888,6432,6433],{"xmlns":890},[892,6434,6435,6439],{},[895,6436,6437],{},[898,6438,5558],{},[902,6440,5558],{"encoding":904},", uvolní-li se omezení o jednotku",[115,6443,6445],{"id":6444},"alternativní-postup","Alternativní postup",[724,6447,6448,6449,6476,6477,6501,6502,6526,6527,6540,6541,1661],{},"Lze-li z ",[883,6450,6452],{"className":6451},[886],[888,6453,6454],{"xmlns":890},[892,6455,6456,6474],{},[895,6457,6458,6460,6462,6464,6466,6468,6470,6472],{},[898,6459,5633],{},[5560,6461,5563],{"stretchy":5562},[898,6463,5566],{},[5560,6465,5570],{"separator":5569},[898,6467,5573],{},[5560,6469,3998],{"stretchy":5562},[5560,6471,5646],{},[5600,6473,5649],{},[902,6475,5652],{"encoding":904}," vyjádřit ",[883,6478,6480],{"className":6479},[886],[888,6481,6482],{"xmlns":890},[892,6483,6484,6498],{},[895,6485,6486,6488,6490,6492,6494,6496],{},[898,6487,5573],{},[5560,6489,5646],{},[898,6491,5573],{},[5560,6493,5563],{"stretchy":5562},[898,6495,5566],{},[5560,6497,3998],{"stretchy":5562},[902,6499,6500],{"encoding":904},"y = y(x)"," (nebo ",[883,6503,6505],{"className":6504},[886],[888,6506,6507],{"xmlns":890},[892,6508,6509,6523],{},[895,6510,6511,6513,6515,6517,6519,6521],{},[898,6512,5566],{},[5560,6514,5646],{},[898,6516,5566],{},[5560,6518,5563],{"stretchy":5562},[898,6520,5573],{},[5560,6522,3998],{"stretchy":5562},[902,6524,6525],{"encoding":904},"x = x(y)","), dosadíme do ",[883,6528,6530],{"className":6529},[886],[888,6531,6532],{"xmlns":890},[892,6533,6534,6538],{},[895,6535,6536],{},[898,6537,5558],{},[902,6539,5558],{"encoding":904}," a převedeme na ",[38,6542,6543],{},"extrém funkce jedné proměnné",[115,6545,6547],{"id":6546},"použití-v-imek","Použití v ImeK",[198,6549,6551],{"id":6550},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,6553,6554,6555,1661],{},"Rozpočtové omezení: ",[883,6556,6558],{"className":6557},[886],[888,6559,6560],{"xmlns":890},[892,6561,6562,6605],{},[895,6563,6564,6572,6574,6583,6589,6591,6599],{},[6018,6565,6566,6569],{},[898,6567,6568],{},"Y",[5560,6570,6571],{},"∗",[5560,6573,5646],{},[5805,6575,6576,6579,6581],{},[898,6577,6578],{},"P",[5600,6580,5602],{},[5560,6582,6571],{},[5594,6584,6585,6587],{},[898,6586,5598],{},[5600,6588,5602],{},[5560,6590,5743],{},[5805,6592,6593,6595,6597],{},[898,6594,6578],{},[5600,6596,5611],{},[5560,6598,6571],{},[5594,6600,6601,6603],{},[898,6602,5598],{},[5600,6604,5611],{},[902,6606,6607],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,6609,6610],{},[883,6611,6613],{"className":6612},[886],[888,6614,6615],{"xmlns":890},[892,6616,6617,6711],{},[895,6618,6619,6621,6623,6629,6631,6637,6639,6641,6643,6645,6647,6649,6655,6657,6663,6665,6667,6669,6671,6677,6679,6687,6693,6695,6703,6709],{},[898,6620,5711],{},[5560,6622,5563],{"stretchy":5562},[5594,6624,6625,6627],{},[898,6626,5598],{},[5600,6628,5602],{},[5560,6630,5570],{"separator":5569},[5594,6632,6633,6635],{},[898,6634,5598],{},[5600,6636,5611],{},[5560,6638,5570],{"separator":5569},[898,6640,5724],{},[5560,6642,3998],{"stretchy":5562},[5560,6644,5646],{},[898,6646,900],{},[5560,6648,5563],{"stretchy":5562},[5594,6650,6651,6653],{},[898,6652,5598],{},[5600,6654,5602],{},[5560,6656,5570],{"separator":5569},[5594,6658,6659,6661],{},[898,6660,5598],{},[5600,6662,5611],{},[5560,6664,3998],{"stretchy":5562},[5560,6666,5743],{},[898,6668,5724],{},[5560,6670,5563],{"stretchy":5562},[6018,6672,6673,6675],{},[898,6674,6568],{},[5560,6676,6571],{},[5560,6678,6084],{},[5805,6680,6681,6683,6685],{},[898,6682,6578],{},[5600,6684,5602],{},[5560,6686,6571],{},[5594,6688,6689,6691],{},[898,6690,5598],{},[5600,6692,5602],{},[5560,6694,6084],{},[5805,6696,6697,6699,6701],{},[898,6698,6578],{},[5600,6700,5611],{},[5560,6702,6571],{},[5594,6704,6705,6707],{},[898,6706,5598],{},[5600,6708,5611],{},[5560,6710,3998],{"stretchy":5562},[902,6712,6713],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,6715,6716,6717,1343,6749,1343,6781,6830,6831,6886,6887,1661],{},"Soustava: ",[883,6718,6720],{"className":6719},[886],[888,6721,6722],{"xmlns":890},[892,6723,6724,6746],{},[895,6725,6726,6734,6736,6738],{},[5805,6727,6728,6730,6732],{},[898,6729,900],{},[5600,6731,5602],{},[5560,6733,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5560,6735,5646],{},[898,6737,5724],{},[5805,6739,6740,6742,6744],{},[898,6741,6578],{},[5600,6743,5602],{},[5560,6745,6571],{},[902,6747,6748],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,6750,6752],{"className":6751},[886],[888,6753,6754],{"xmlns":890},[892,6755,6756,6778],{},[895,6757,6758,6766,6768,6770],{},[5805,6759,6760,6762,6764],{},[898,6761,900],{},[5600,6763,5611],{},[5560,6765,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5560,6767,5646],{},[898,6769,5724],{},[5805,6771,6772,6774,6776],{},[898,6773,6578],{},[5600,6775,5611],{},[5560,6777,6571],{},[902,6779,6780],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,6782,6784],{"className":6783},[886],[888,6785,6786],{"xmlns":890},[892,6787,6788,6828],{},[895,6789,6790,6796,6798,6806,6812,6814,6822],{},[6018,6791,6792,6794],{},[898,6793,6568],{},[5560,6795,6571],{},[5560,6797,5646],{},[5805,6799,6800,6802,6804],{},[898,6801,6578],{},[5600,6803,5602],{},[5560,6805,6571],{},[5594,6807,6808,6810],{},[898,6809,5598],{},[5600,6811,5602],{},[5560,6813,5743],{},[5805,6815,6816,6818,6820],{},[898,6817,6578],{},[5600,6819,5611],{},[5560,6821,6571],{},[5594,6823,6824,6826],{},[898,6825,5598],{},[5600,6827,5611],{},[902,6829,6607],{"encoding":904},". Z prvních dvou: ",[883,6832,6834],{"className":6833},[886],[888,6835,6836],{"xmlns":890},[892,6837,6838,6883],{},[895,6839,6840,6861,6863],{},[6841,6842,6843],"mstyle",{"scriptlevel":5649,"displaystyle":5562},[6349,6844,6845,6853],{},[5805,6846,6847,6849,6851],{},[898,6848,900],{},[5600,6850,5602],{},[5560,6852,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5805,6854,6855,6857,6859],{},[898,6856,900],{},[5600,6858,5611],{},[5560,6860,5815],{"mathvariant":5813,"lspace":5814,"rspace":5814},[5560,6862,5646],{},[6841,6864,6865],{"scriptlevel":5649,"displaystyle":5562},[6349,6866,6867,6875],{},[5805,6868,6869,6871,6873],{},[898,6870,6578],{},[5600,6872,5602],{},[5560,6874,6571],{},[5805,6876,6877,6879,6881],{},[898,6878,6578],{},[5600,6880,5611],{},[5560,6882,6571],{},[902,6884,6885],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,6888,6890],{"className":6889},[886],[888,6891,6892],{"xmlns":890},[892,6893,6894,6930],{},[895,6895,6896,6899,6902,6905,6908,6910],{},[898,6897,6898],{},"M",[898,6900,6901],{},"R",[898,6903,6904],{},"C",[898,6906,6907],{},"S",[5560,6909,5646],{},[6841,6911,6912],{"scriptlevel":5649,"displaystyle":5562},[6349,6913,6914,6922],{},[5805,6915,6916,6918,6920],{},[898,6917,6578],{},[5600,6919,5602],{},[5560,6921,6571],{},[5805,6923,6924,6926,6928],{},[898,6925,6578],{},[5600,6927,5611],{},[5560,6929,6571],{},[902,6931,6932],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,6934,6936],{"id":6935},"minimalizace-výdajů","Minimalizace výdajů",[724,6938,6939,6940,1661],{},"Podmínka dané užitečnosti ",[883,6941,6943],{"className":6942},[886],[888,6944,6945],{"xmlns":890},[892,6946,6947,6977],{},[895,6948,6949,6955,6957,6959,6961,6967,6969,6975],{},[6018,6950,6951,6953],{},[898,6952,900],{},[5560,6954,6571],{},[5560,6956,5646],{},[898,6958,900],{},[5560,6960,5563],{"stretchy":5562},[5594,6962,6963,6965],{},[898,6964,5598],{},[5600,6966,5602],{},[5560,6968,5570],{"separator":5569},[5594,6970,6971,6973],{},[898,6972,5598],{},[5600,6974,5611],{},[5560,6976,3998],{"stretchy":5562},[902,6978,6979],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,6981,6982],{},[883,6983,6985],{"className":6984},[886],[888,6986,6987],{"xmlns":890},[892,6988,6989,7083],{},[895,6990,6991,6993,6995,7001,7003,7009,7011,7013,7015,7017,7025,7031,7033,7041,7047,7049,7051,7053,7059,7061,7063,7065,7071,7073,7079,7081],{},[898,6992,5711],{},[5560,6994,5563],{"stretchy":5562},[5594,6996,6997,6999],{},[898,6998,5598],{},[5600,7000,5602],{},[5560,7002,5570],{"separator":5569},[5594,7004,7005,7007],{},[898,7006,5598],{},[5600,7008,5611],{},[5560,7010,5570],{"separator":5569},[898,7012,5724],{},[5560,7014,3998],{"stretchy":5562},[5560,7016,5646],{},[5805,7018,7019,7021,7023],{},[898,7020,6578],{},[5600,7022,5602],{},[5560,7024,6571],{},[5594,7026,7027,7029],{},[898,7028,5598],{},[5600,7030,5602],{},[5560,7032,5743],{},[5805,7034,7035,7037,7039],{},[898,7036,6578],{},[5600,7038,5611],{},[5560,7040,6571],{},[5594,7042,7043,7045],{},[898,7044,5598],{},[5600,7046,5611],{},[5560,7048,5743],{},[898,7050,5724],{},[5560,7052,5563],{"stretchy":5562},[6018,7054,7055,7057],{},[898,7056,900],{},[5560,7058,6571],{},[5560,7060,6084],{},[898,7062,900],{},[5560,7064,5563],{"stretchy":5562},[5594,7066,7067,7069],{},[898,7068,5598],{},[5600,7070,5602],{},[5560,7072,5570],{"separator":5569},[5594,7074,7075,7077],{},[898,7076,5598],{},[5600,7078,5611],{},[5560,7080,3998],{"stretchy":5562},[5560,7082,3998],{"stretchy":5562},[902,7084,7085],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,7087,7088,7089,1661],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,7090,7092],{"className":7091},[886],[888,7093,7094],{"xmlns":890},[892,7095,7096,7135],{},[895,7097,7098,7105,7107,7113,7115,7121,7123,7129,7131,7133],{},[5594,7099,7100,7102],{},[898,7101,5598],{},[898,7103,7104],{},"i",[5560,7106,5646],{},[5594,7108,7109,7111],{},[898,7110,5950],{},[898,7112,7104],{},[5560,7114,5563],{"stretchy":5562},[5594,7116,7117,7119],{},[898,7118,6578],{},[5600,7120,5602],{},[5560,7122,5570],{"separator":5569},[5594,7124,7125,7127],{},[898,7126,6578],{},[5600,7128,5611],{},[5560,7130,5570],{"separator":5569},[898,7132,900],{},[5560,7134,3998],{"stretchy":5562},[902,7136,7137],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,7139,7141],{"id":7140},"navigace","Navigace",[120,7143,7144,7152,7161,7170],{},[123,7145,7146,2259,7149],{},[38,7147,7148],{},"Předchozí:",[207,7150,784],{"className":7151,"dataFsResolvedFilePath":782,"href":783},[210],[123,7153,7154,2259,7157],{},[38,7155,7156],{},"Navazující:",[207,7158,7160],{"className":7159,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[123,7162,7163,2259,7166,7169],{},[38,7164,7165],{},"Aplikace v kurzu:",[207,7167,880],{"className":7168,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,7171,7172,2259,7175,1343,7178,7181],{},[38,7173,7174],{},"Souvislosti:",[207,7176,936],{"className":7177,"dataFsResolvedFilePath":934,"href":935},[210],[207,7179,1400],{"className":7180,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":7183},[7184,7185,7186,7187,7188,7189,7193],{"id":2874,"depth":642,"text":2875},{"id":5788,"depth":642,"text":5789},{"id":5935,"depth":642,"text":5936},{"id":6331,"depth":642,"text":6332},{"id":6444,"depth":642,"text":6445},{"id":6546,"depth":642,"text":6547,"children":7190},[7191,7192],{"id":6550,"depth":649,"text":6551},{"id":6935,"depth":649,"text":6936},{"id":7140,"depth":642,"text":7141},[1128,1601],"Hledáme extrém funkce f(x,y)f(x, y) (resp. U(Q1,Q2)U(Q_1, Q_2) apod.) podmíněný rovnicí g(x,y)=0g(x, y) = 0. V matematické ekonomii se používá pro:",{},"\u002Ftopics\u002Flagrangeova-metoda",{"title":5538,"description":7195},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,7202,7203],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":7206,"title":1400,"body":7207,"course":1601,"courses":659,"created":2822,"description":8457,"extension":661,"meta":8458,"navigation":664,"path":8459,"seo":8460,"sources":8461,"stem":8462,"tags":8463,"type":2835,"updated":677,"__hash__":8466},"topics\u002Ftopics\u002Foptimalizace.md",{"type":9,"value":7208,"toc":8433},[7209,7211,7222,7233,7235,7238,7258,7263,7269,7281,7285,7367,7373,7377,7446,7450,7490,7492,7496,7502,7505,7510,7519,7524,7624,7629,7670,7677,7729,7734,7800,7805,7820,7822,7828,7831,7836,7845,7855,7864,7869,7908,7910,7916,7920,7929,7937,7942,7967,7972,7997,7999,8005,8009,8018,8028,8033,8058,8060,8066,8069,8073,8082,8090,8135,8140,8160,8162,8168,8172,8181,8186,8288,8293,8333,8335,8339,8390,8392,8406,8408,8411,8416,8431],[12,7210,1400],{"id":1619},[724,7212,7213,7214,7217,7218,7221],{},"Optimalizace je matematická disciplína, ve které hledáme minimum (resp. maximum) dané funkce f(x) na dané množině M. Tato funkce se nazývá ",[38,7215,7216],{},"účelová"," či ",[38,7219,7220],{},"cílová",". Množina přípustných řešení bývá typicky popsána omezeními — soustavou rovnic nebo nerovnic.",[724,7223,1645,7224,1343,7227,1343,7230,1661],{},[207,7225,3946],{"className":7226,"dataFsResolvedFilePath":1282,"href":1283},[210],[207,7228,1657],{"className":7229,"dataFsResolvedFilePath":1383,"href":1384},[210],[207,7231,1620],{"className":7232,"dataFsResolvedFilePath":1303,"href":1304},[210],[115,7234,5221],{"id":5220},[724,7236,7237],{},"Každá optimalizační úloha obsahuje tři složky:",[120,7239,7240,7246,7252],{},[123,7241,7242,7245],{},[38,7243,7244],{},"Stavové (rozhodovací) proměnné"," (x₁, x₂, ..., xₙ) — hodnoty, které měníme",[123,7247,7248,7251],{},[38,7249,7250],{},"Účelová (cílová) funkce"," f(x) — výraz, který minimalizujeme nebo maximalizujeme",[123,7253,7254,7257],{},[38,7255,7256],{},"Omezující podmínky"," — definují přípustnou množinu M",[724,7259,7260],{},[38,7261,7262],{},"Obecná formulace minimalizační úlohy:",[1733,7264,7267],{"className":7265,"code":7266,"language":1738},[1736],"minimalizovat f(x)\nza podmínek:\n  g(x) ≤ 0      (nerovnostní omezení)\n  h(x) = 0      (rovnostní omezení)\n  lb ≤ x ≤ ub   (meze proměnných)\n",[1740,7268,7266],{"__ignoreMap":641},[724,7270,7271,2259,7274,7277,7278,1661],{},[38,7272,7273],{},"Maximalizace = negace:",[1740,7275,7276],{},"max f(x)"," je ekvivalentní ",[1740,7279,7280],{},"min(−f(x))",[115,7282,7284],{"id":7283},"typy-omezujících-podmínek-v-matlabu","Typy omezujících podmínek (v MATLABu)",[16,7286,7287,7300],{},[19,7288,7289],{},[22,7290,7291,7294,7297],{},[25,7292,7293],{},"Typ omezení",[25,7295,7296],{},"Zápis v MATLABu",[25,7298,7299],{},"Popis",[30,7301,7302,7315,7328,7341,7354],{},[22,7303,7304,7307,7312],{},[35,7305,7306],{},"Lineární nerovnostní",[35,7308,7309],{},[1740,7310,7311],{},"A·x ≤ b",[35,7313,7314],{},"Matice A, vektor b",[22,7316,7317,7320,7325],{},[35,7318,7319],{},"Lineární rovnostní",[35,7321,7322],{},[1740,7323,7324],{},"Aeq·x = beq",[35,7326,7327],{},"Matice Aeq, vektor beq",[22,7329,7330,7333,7338],{},[35,7331,7332],{},"Nelineární nerovnostní",[35,7334,7335],{},[1740,7336,7337],{},"c(x) ≤ 0",[35,7339,7340],{},"Funkce vracející vektor c",[22,7342,7343,7346,7351],{},[35,7344,7345],{},"Nelineární rovnostní",[35,7347,7348],{},[1740,7349,7350],{},"ceq(x) = 0",[35,7352,7353],{},"Funkce vracející vektor ceq",[22,7355,7356,7359,7364],{},[35,7357,7358],{},"Meze proměnných",[35,7360,7361],{},[1740,7362,7363],{},"lb ≤ x ≤ ub",[35,7365,7366],{},"Dolní a horní meze",[724,7368,7369,7370,1661],{},"Nepotřebná omezení zadáváme jako ",[1740,7371,7372],{},"[]",[115,7374,7376],{"id":7375},"typy-optimalizačních-úloh","Typy optimalizačních úloh",[16,7378,7379,7390],{},[19,7380,7381],{},[22,7382,7383,7385,7387],{},[25,7384,4665],{},[25,7386,7299],{},[25,7388,7389],{},"MATLAB solver",[30,7391,7392,7405,7421,7434],{},[22,7393,7394,7397,7400],{},[35,7395,7396],{},"Lineární programování (LP)",[35,7398,7399],{},"f(x) i omezení jsou lineární",[35,7401,7402],{},[1740,7403,7404],{},"linprog",[22,7406,7407,7410,7413],{},[35,7408,7409],{},"Nelineární programování (NLP)",[35,7411,7412],{},"f(x) nebo omezení jsou nelineární",[35,7414,7415,1343,7418],{},[1740,7416,7417],{},"fmincon",[1740,7419,7420],{},"fminsearch",[22,7422,7423,7426,7429],{},[35,7424,7425],{},"Celočíselné lineární (MILP)",[35,7427,7428],{},"LP, kde proměnné jsou celá čísla",[35,7430,7431],{},[1740,7432,7433],{},"intlinprog",[22,7435,7436,7438,7441],{},[35,7437,4726],{},[35,7439,7440],{},"Diskrétní množina řešení",[35,7442,7443],{},[1740,7444,7445],{},"ga",[115,7447,7449],{"id":7448},"lokální-vs-globální-optimum","Lokální vs. globální optimum",[120,7451,7452,7458,7464,7475],{},[123,7453,7454,7457],{},[38,7455,7456],{},"Globální minimum"," — absolutně nejnižší hodnota f(x) v celém definičním oboru",[123,7459,7460,7463],{},[38,7461,7462],{},"Lokální minimum"," — nejnižší hodnota v okolí, ale ne nutně nejnižší ze všech",[123,7465,7466,1343,7468,7470,7471,7474],{},[1740,7467,7417],{},[1740,7469,7420],{}," nacházejí ",[38,7472,7473],{},"lokální"," minima — výsledek závisí na počátečním bodu x0",[123,7476,7477,7478,7481,7482,1343,7484,1343,7487],{},"Pro ",[38,7479,7480],{},"globální"," optimalizaci: ",[1740,7483,7445],{},[1740,7485,7486],{},"GlobalSearch",[1740,7488,7489],{},"MultiStart",[1720,7491],{},[115,7493,7495],{"id":7494},"matlab-optimization-toolbox-příkazy","MATLAB Optimization Toolbox — příkazy",[198,7497,7499,7501],{"id":7498},"fmincon-nelineární-optimalizace-s-omezeními",[1740,7500,7417],{}," — nelineární optimalizace s omezeními",[724,7503,7504],{},"Nejuniverzálnější solver. Hledá minimum nelineární funkce s lineárními i nelineárními omezeními a mezemi.",[724,7506,7507],{},[38,7508,7509],{},"Plná syntaxe:",[1733,7511,7513],{"className":2455,"code":7512,"language":2457,"meta":641,"style":641},"[x, fval, exitflag, output] = fmincon(fun, x0, A, b, Aeq, beq, lb, ub, nonlcon, options)\n",[1740,7514,7515],{"__ignoreMap":641},[883,7516,7517],{"class":2462,"line":2463},[883,7518,7512],{},[724,7520,7521],{},[38,7522,7523],{},"Parametry:",[16,7525,7526,7535],{},[19,7527,7528],{},[22,7529,7530,7533],{},[25,7531,7532],{},"Parametr",[25,7534,7299],{},[30,7536,7537,7550,7560,7572,7585,7598,7611],{},[22,7538,7539,7544],{},[35,7540,7541],{},[1740,7542,7543],{},"fun",[35,7545,7546,7547,3998],{},"Účelová funkce (function handle ",[1740,7548,7549],{},"@",[22,7551,7552,7557],{},[35,7553,7554],{},[1740,7555,7556],{},"x0",[35,7558,7559],{},"Počáteční bod (vektor)",[22,7561,7562,7569],{},[35,7563,7564,1343,7567],{},[1740,7565,7566],{},"A",[1740,7568,6171],{},[35,7570,7571],{},"Lineární nerovnostní omezení: A·x ≤ b",[22,7573,7574,7582],{},[35,7575,7576,1343,7579],{},[1740,7577,7578],{},"Aeq",[1740,7580,7581],{},"beq",[35,7583,7584],{},"Lineární rovnostní omezení: Aeq·x = beq",[22,7586,7587,7595],{},[35,7588,7589,1343,7592],{},[1740,7590,7591],{},"lb",[1740,7593,7594],{},"ub",[35,7596,7597],{},"Dolní a horní meze proměnných",[22,7599,7600,7605],{},[35,7601,7602],{},[1740,7603,7604],{},"nonlcon",[35,7606,7607,7608],{},"Nelineární omezení — function handle vracející ",[883,7609,7610],{},"c, ceq",[22,7612,7613,7618],{},[35,7614,7615],{},[1740,7616,7617],{},"options",[35,7619,7620,7621],{},"Nastavení z ",[1740,7622,7623],{},"optimoptions",[724,7625,7626],{},[38,7627,7628],{},"Výstupy:",[16,7630,7631,7639],{},[19,7632,7633],{},[22,7634,7635,7637],{},[25,7636,5046],{},[25,7638,7299],{},[30,7640,7641,7650,7660],{},[22,7642,7643,7647],{},[35,7644,7645],{},[1740,7646,5566],{},[35,7648,7649],{},"Optimální řešení",[22,7651,7652,7657],{},[35,7653,7654],{},[1740,7655,7656],{},"fval",[35,7658,7659],{},"Hodnota f(x) v optimu",[22,7661,7662,7667],{},[35,7663,7664],{},[1740,7665,7666],{},"exitflag",[35,7668,7669],{},"Důvod ukončení (1 = konvergence, záporné = selhání)",[724,7671,7672],{},[38,7673,7674,7675,5697],{},"Algoritmy ",[1740,7676,7417],{},[16,7678,7679,7687],{},[19,7680,7681],{},[22,7682,7683,7685],{},[25,7684,2187],{},[25,7686,4568],{},[30,7688,7689,7699,7709,7719],{},[22,7690,7691,7696],{},[35,7692,7693],{},[1740,7694,7695],{},"'interior-point'",[35,7697,7698],{},"Výchozí; velké problémy s mnoha proměnnými",[22,7700,7701,7706],{},[35,7702,7703],{},[1740,7704,7705],{},"'sqp'",[35,7707,7708],{},"Dobrá volba pro většinu problémů",[22,7710,7711,7716],{},[35,7712,7713],{},[1740,7714,7715],{},"'active-set'",[35,7717,7718],{},"Nehladká omezení",[22,7720,7721,7726],{},[35,7722,7723],{},[1740,7724,7725],{},"'trust-region-reflective'",[35,7727,7728],{},"Pouze meze nebo lineární rovnosti",[724,7730,7731],{},[38,7732,7733],{},"Příklad — minimalizace výrobních nákladů:",[1733,7735,7737],{"className":2455,"code":7736,"language":2457,"meta":641,"style":641},"% f(x) = 3*x1 + 5*x2\nfun = @(x) 3*x(1) + 5*x(2);\nx0 = [5, 5];\n\n% Omezení: x1 + x2 \u003C= 20, x1 >= 4, x2 >= 3\nA = [1, 1; -1, 0; 0, -1];\nb = [20; -4; -3];\nlb = [0, 0];\nub = [20, 20];\n\noptions = optimoptions('fmincon', 'Display', 'final', 'Algorithm', 'sqp');\n[x, fval] = fmincon(fun, x0, A, b, [], [], lb, ub, [], options);\n",[1740,7738,7739,7744,7749,7754,7758,7763,7768,7773,7778,7784,7789,7794],{"__ignoreMap":641},[883,7740,7741],{"class":2462,"line":2463},[883,7742,7743],{},"% f(x) = 3*x1 + 5*x2\n",[883,7745,7746],{"class":2462,"line":642},[883,7747,7748],{},"fun = @(x) 3*x(1) + 5*x(2);\n",[883,7750,7751],{"class":2462,"line":649},[883,7752,7753],{},"x0 = [5, 5];\n",[883,7755,7756],{"class":2462,"line":2479},[883,7757,2476],{"emptyLinePlaceholder":664},[883,7759,7760],{"class":2462,"line":2485},[883,7761,7762],{},"% Omezení: x1 + x2 \u003C= 20, x1 >= 4, x2 >= 3\n",[883,7764,7765],{"class":2462,"line":2491},[883,7766,7767],{},"A = [1, 1; -1, 0; 0, -1];\n",[883,7769,7770],{"class":2462,"line":2497},[883,7771,7772],{},"b = [20; -4; -3];\n",[883,7774,7775],{"class":2462,"line":2503},[883,7776,7777],{},"lb = [0, 0];\n",[883,7779,7781],{"class":2462,"line":7780},9,[883,7782,7783],{},"ub = [20, 20];\n",[883,7785,7787],{"class":2462,"line":7786},10,[883,7788,2476],{"emptyLinePlaceholder":664},[883,7790,7791],{"class":2462,"line":2839},[883,7792,7793],{},"options = optimoptions('fmincon', 'Display', 'final', 'Algorithm', 'sqp');\n",[883,7795,7797],{"class":2462,"line":7796},12,[883,7798,7799],{},"[x, fval] = fmincon(fun, x0, A, b, [], [], lb, ub, [], options);\n",[724,7801,7802],{},[38,7803,7804],{},"Nelineární omezení (syntax nonlcon):",[1733,7806,7808],{"className":2455,"code":7807,"language":2457,"meta":641,"style":641},"% Musí vracet [c, ceq] — c(x)\u003C=0 a ceq(x)=0\nnonlcon = @(x) deal(25 - x(1)*x(2)*x(3)*x(4), sum(x.^2) - 40);\n",[1740,7809,7810,7815],{"__ignoreMap":641},[883,7811,7812],{"class":2462,"line":2463},[883,7813,7814],{},"% Musí vracet [c, ceq] — c(x)\u003C=0 a ceq(x)=0\n",[883,7816,7817],{"class":2462,"line":642},[883,7818,7819],{},"nonlcon = @(x) deal(25 - x(1)*x(2)*x(3)*x(4), sum(x.^2) - 40);\n",[1720,7821],{},[198,7823,7825,7827],{"id":7824},"fminsearch-optimalizace-bez-omezení-nelder-mead",[1740,7826,7420],{}," — optimalizace bez omezení (Nelder-Mead)",[724,7829,7830],{},"Nepotřebuje gradient (derivative-free). Vhodné pro funkce s obtížně spočitatelným gradientem. Pracuje se simplexem n+1 bodů.",[724,7832,7833],{},[38,7834,7835],{},"Syntaxe:",[1733,7837,7839],{"className":2455,"code":7838,"language":2457,"meta":641,"style":641},"[x, fval] = fminsearch(fun, x0, options)\n",[1740,7840,7841],{"__ignoreMap":641},[883,7842,7843],{"class":2462,"line":2463},[883,7844,7838],{},[724,7846,7847,7848,7851,7852,7854],{},"Používá ",[1740,7849,7850],{},"optimset"," (ne ",[1740,7853,7623],{},"):",[1733,7856,7858],{"className":2455,"code":7857,"language":2457,"meta":641,"style":641},"options = optimset('MaxIter', 1000, 'TolFun', 1e-8, 'TolX', 1e-8, 'Display', 'iter');\n",[1740,7859,7860],{"__ignoreMap":641},[883,7861,7862],{"class":2462,"line":2463},[883,7863,7857],{},[724,7865,7866],{},[38,7867,7868],{},"Příklady:",[1733,7870,7872],{"className":2455,"code":7871,"language":2457,"meta":641,"style":641},"% Kvadratická funkce\nfun = @(x) (x - 3)^2 + 2;\n[x, fval] = fminsearch(fun, 0)     % → x≈3, fval≈2\n\n% Rosenbrock (2 proměnné)\nrosenbrock = @(x) (1-x(1))^2 + 100*(x(2)-x(1)^2)^2;\n[x, fval] = fminsearch(rosenbrock, [-1, -1])    % → x≈[1,1]\n",[1740,7873,7874,7879,7884,7889,7893,7898,7903],{"__ignoreMap":641},[883,7875,7876],{"class":2462,"line":2463},[883,7877,7878],{},"% Kvadratická funkce\n",[883,7880,7881],{"class":2462,"line":642},[883,7882,7883],{},"fun = @(x) (x - 3)^2 + 2;\n",[883,7885,7886],{"class":2462,"line":649},[883,7887,7888],{},"[x, fval] = fminsearch(fun, 0)     % → x≈3, fval≈2\n",[883,7890,7891],{"class":2462,"line":2479},[883,7892,2476],{"emptyLinePlaceholder":664},[883,7894,7895],{"class":2462,"line":2485},[883,7896,7897],{},"% Rosenbrock (2 proměnné)\n",[883,7899,7900],{"class":2462,"line":2491},[883,7901,7902],{},"rosenbrock = @(x) (1-x(1))^2 + 100*(x(2)-x(1)^2)^2;\n",[883,7904,7905],{"class":2462,"line":2497},[883,7906,7907],{},"[x, fval] = fminsearch(rosenbrock, [-1, -1])    % → x≈[1,1]\n",[1720,7909],{},[198,7911,7913,7915],{"id":7912},"linprog-lineární-programování",[1740,7914,7404],{}," — lineární programování",[724,7917,7918],{},[38,7919,7835],{},[1733,7921,7923],{"className":2455,"code":7922,"language":2457,"meta":641,"style":641},"[x, fval] = linprog(f, A, b, Aeq, beq, lb, ub)\n",[1740,7924,7925],{"__ignoreMap":641},[883,7926,7927],{"class":2462,"line":2463},[883,7928,7922],{},[724,7930,7931,7933,7934,1661],{},[1740,7932,5558],{}," je vektor koeficientů účelové funkce — minimalizuje ",[1740,7935,7936],{},"f' · x",[724,7938,7939],{},[38,7940,7941],{},"Minimalizace nákladů:",[1733,7943,7945],{"className":2455,"code":7944,"language":2457,"meta":641,"style":641},"f = [2; 3];                  % minimalizuje 2*x1 + 3*x2\nA = [1, 1; 2, 1]; b = [10; 14];\nlb = [0; 0];\n[x, fval] = linprog(f, A, b, [], [], lb)\n",[1740,7946,7947,7952,7957,7962],{"__ignoreMap":641},[883,7948,7949],{"class":2462,"line":2463},[883,7950,7951],{},"f = [2; 3];                  % minimalizuje 2*x1 + 3*x2\n",[883,7953,7954],{"class":2462,"line":642},[883,7955,7956],{},"A = [1, 1; 2, 1]; b = [10; 14];\n",[883,7958,7959],{"class":2462,"line":649},[883,7960,7961],{},"lb = [0; 0];\n",[883,7963,7964],{"class":2462,"line":2479},[883,7965,7966],{},"[x, fval] = linprog(f, A, b, [], [], lb)\n",[724,7968,7969],{},[38,7970,7971],{},"Maximalizace zisku (negace f):",[1733,7973,7975],{"className":2455,"code":7974,"language":2457,"meta":641,"style":641},"% max z(x) = 12*x1 + 7*x2 → min -z(x)\nf = [-12; -7];\n[x, neg_zisk] = linprog(f, A, b, [], [], lb);\nmax_zisk = -neg_zisk;\n",[1740,7976,7977,7982,7987,7992],{"__ignoreMap":641},[883,7978,7979],{"class":2462,"line":2463},[883,7980,7981],{},"% max z(x) = 12*x1 + 7*x2 → min -z(x)\n",[883,7983,7984],{"class":2462,"line":642},[883,7985,7986],{},"f = [-12; -7];\n",[883,7988,7989],{"class":2462,"line":649},[883,7990,7991],{},"[x, neg_zisk] = linprog(f, A, b, [], [], lb);\n",[883,7993,7994],{"class":2462,"line":2479},[883,7995,7996],{},"max_zisk = -neg_zisk;\n",[1720,7998],{},[198,8000,8002,8004],{"id":8001},"intlinprog-celočíselné-lineární-programování-milp",[1740,8003,7433],{}," — celočíselné lineární programování (MILP)",[724,8006,8007],{},[38,8008,7835],{},[1733,8010,8012],{"className":2455,"code":8011,"language":2457,"meta":641,"style":641},"[x, fval] = intlinprog(f, intcon, A, b, Aeq, beq, lb, ub)\n",[1740,8013,8014],{"__ignoreMap":641},[883,8015,8016],{"class":2462,"line":2463},[883,8017,8011],{},[724,8019,8020,8023,8024,8027],{},[1740,8021,8022],{},"intcon"," = vektor indexů celočíselných proměnných (např. ",[1740,8025,8026],{},"[1, 3]"," = x1 a x3 jsou celá čísla).",[724,8029,8030],{},[38,8031,8032],{},"Binární proměnné (lb=0, ub=1):",[1733,8034,8036],{"className":2455,"code":8035,"language":2457,"meta":641,"style":641},"f = [5; 8; 3; 6];\nintcon = [1, 2, 3, 4];    % všechny proměnné binární\nlb = zeros(4,1); ub = ones(4,1);\n[x, fval] = intlinprog(f, intcon, A, b, [], [], lb, ub)\n",[1740,8037,8038,8043,8048,8053],{"__ignoreMap":641},[883,8039,8040],{"class":2462,"line":2463},[883,8041,8042],{},"f = [5; 8; 3; 6];\n",[883,8044,8045],{"class":2462,"line":642},[883,8046,8047],{},"intcon = [1, 2, 3, 4];    % všechny proměnné binární\n",[883,8049,8050],{"class":2462,"line":649},[883,8051,8052],{},"lb = zeros(4,1); ub = ones(4,1);\n",[883,8054,8055],{"class":2462,"line":2479},[883,8056,8057],{},"[x, fval] = intlinprog(f, intcon, A, b, [], [], lb, ub)\n",[1720,8059],{},[198,8061,8063,8065],{"id":8062},"ga-genetický-algoritmus-global-optimization-toolbox",[1740,8064,7445],{}," — genetický algoritmus (Global Optimization Toolbox)",[724,8067,8068],{},"Hledá globální minimum. Vhodný pro nekonvexní, nehladké nebo diskrétní problémy.",[724,8070,8071],{},[38,8072,7835],{},[1733,8074,8076],{"className":2455,"code":8075,"language":2457,"meta":641,"style":641},"[x, fval] = ga(fun, nvars, A, b, Aeq, beq, lb, ub, nonlcon, intcon, options)\n",[1740,8077,8078],{"__ignoreMap":641},[883,8079,8080],{"class":2462,"line":2463},[883,8081,8075],{},[724,8083,8084],{},[38,8085,8086,8087,5697],{},"Klíčové parametry ",[1740,8088,8089],{},"optimoptions('ga', ...)",[1733,8091,8093],{"className":2455,"code":8092,"language":2457,"meta":641,"style":641},"options = optimoptions('ga', ...\n    'PopulationSize',      100, ...    % velikost populace\n    'MaxGenerations',      300, ...    % max počet generací\n    'CrossoverFraction',   0.8, ...    % podíl křížení\n    'EliteCount',          5, ...      % elitní jedinci (přecházejí přímo)\n    'MaxStallGenerations', 50, ...     % zastavení po N generacích bez zlepšení\n    'Display',             'iter', ...\n    'PlotFcn',             @gaplotbestfun);\n",[1740,8094,8095,8100,8105,8110,8115,8120,8125,8130],{"__ignoreMap":641},[883,8096,8097],{"class":2462,"line":2463},[883,8098,8099],{},"options = optimoptions('ga', ...\n",[883,8101,8102],{"class":2462,"line":642},[883,8103,8104],{},"    'PopulationSize',      100, ...    % velikost populace\n",[883,8106,8107],{"class":2462,"line":649},[883,8108,8109],{},"    'MaxGenerations',      300, ...    % max počet generací\n",[883,8111,8112],{"class":2462,"line":2479},[883,8113,8114],{},"    'CrossoverFraction',   0.8, ...    % podíl křížení\n",[883,8116,8117],{"class":2462,"line":2485},[883,8118,8119],{},"    'EliteCount',          5, ...      % elitní jedinci (přecházejí přímo)\n",[883,8121,8122],{"class":2462,"line":2491},[883,8123,8124],{},"    'MaxStallGenerations', 50, ...     % zastavení po N generacích bez zlepšení\n",[883,8126,8127],{"class":2462,"line":2497},[883,8128,8129],{},"    'Display',             'iter', ...\n",[883,8131,8132],{"class":2462,"line":2503},[883,8133,8134],{},"    'PlotFcn',             @gaplotbestfun);\n",[724,8136,8137],{},[38,8138,8139],{},"Příklad — globální optimum multimodální funkce:",[1733,8141,8143],{"className":2455,"code":8142,"language":2457,"meta":641,"style":641},"% Rastriginova funkce má mnoho lokálních minim\nrastrigin = @(x) 10*numel(x) + sum(x.^2 - 10*cos(2*pi*x));\n[x, fval] = ga(rastrigin, 2)    % ga najde globální minimum\n",[1740,8144,8145,8150,8155],{"__ignoreMap":641},[883,8146,8147],{"class":2462,"line":2463},[883,8148,8149],{},"% Rastriginova funkce má mnoho lokálních minim\n",[883,8151,8152],{"class":2462,"line":642},[883,8153,8154],{},"rastrigin = @(x) 10*numel(x) + sum(x.^2 - 10*cos(2*pi*x));\n",[883,8156,8157],{"class":2462,"line":649},[883,8158,8159],{},"[x, fval] = ga(rastrigin, 2)    % ga najde globální minimum\n",[1720,8161],{},[198,8163,8165,8167],{"id":8164},"optimoptions-nastavení-parametrů-solverů",[1740,8166,7623],{}," — nastavení parametrů solverů",[724,8169,8170],{},[38,8171,7835],{},[1733,8173,8175],{"className":2455,"code":8174,"language":2457,"meta":641,"style":641},"options = optimoptions('SolverName', 'ParamName', value, ...)\n",[1740,8176,8177],{"__ignoreMap":641},[883,8178,8179],{"class":2462,"line":2463},[883,8180,8174],{},[724,8182,8183],{},[38,8184,8185],{},"Klíčové parametry zastavení:",[16,8187,8188,8199],{},[19,8189,8190],{},[22,8191,8192,8194,8197],{},[25,8193,7532],{},[25,8195,8196],{},"API",[25,8198,7299],{},[30,8200,8201,8215,8229,8243,8257,8271],{},[22,8202,8203,8208,8212],{},[35,8204,8205],{},[1740,8206,8207],{},"MaxIterations",[35,8209,8210],{},[1740,8211,7623],{},[35,8213,8214],{},"Max počet iterací",[22,8216,8217,8222,8226],{},[35,8218,8219],{},[1740,8220,8221],{},"MaxFunctionEvaluations",[35,8223,8224],{},[1740,8225,7623],{},[35,8227,8228],{},"Max počet vyhodnocení funkce",[22,8230,8231,8236,8240],{},[35,8232,8233],{},[1740,8234,8235],{},"OptimalityTolerance",[35,8237,8238],{},[1740,8239,7623],{},[35,8241,8242],{},"Tolerance normy gradientu (dříve TolFun)",[22,8244,8245,8250,8254],{},[35,8246,8247],{},[1740,8248,8249],{},"StepTolerance",[35,8251,8252],{},[1740,8253,7623],{},[35,8255,8256],{},"Tolerance kroku\u002Fzměny x (dříve TolX)",[22,8258,8259,8264,8268],{},[35,8260,8261],{},[1740,8262,8263],{},"ConstraintTolerance",[35,8265,8266],{},[1740,8267,7623],{},[35,8269,8270],{},"Max přípustné porušení omezení",[22,8272,8273,8281,8285],{},[35,8274,8275,1343,8278],{},[1740,8276,8277],{},"TolFun",[1740,8279,8280],{},"TolX",[35,8282,8283],{},[1740,8284,7850],{},[35,8286,8287],{},"Starší API pro fminsearch\u002Ffminbnd",[724,8289,8290],{},[38,8291,8292],{},"Typické nastavení:",[1733,8294,8296],{"className":2455,"code":8295,"language":2457,"meta":641,"style":641},"options = optimoptions('fmincon', ...\n    'Algorithm',              'sqp', ...\n    'Display',                'iter', ...\n    'MaxIterations',          1000, ...\n    'MaxFunctionEvaluations', 3000, ...\n    'OptimalityTolerance',    1e-8, ...\n    'StepTolerance',          1e-8);\n",[1740,8297,8298,8303,8308,8313,8318,8323,8328],{"__ignoreMap":641},[883,8299,8300],{"class":2462,"line":2463},[883,8301,8302],{},"options = optimoptions('fmincon', ...\n",[883,8304,8305],{"class":2462,"line":642},[883,8306,8307],{},"    'Algorithm',              'sqp', ...\n",[883,8309,8310],{"class":2462,"line":649},[883,8311,8312],{},"    'Display',                'iter', ...\n",[883,8314,8315],{"class":2462,"line":2479},[883,8316,8317],{},"    'MaxIterations',          1000, ...\n",[883,8319,8320],{"class":2462,"line":2485},[883,8321,8322],{},"    'MaxFunctionEvaluations', 3000, ...\n",[883,8324,8325],{"class":2462,"line":2491},[883,8326,8327],{},"    'OptimalityTolerance',    1e-8, ...\n",[883,8329,8330],{"class":2462,"line":2497},[883,8331,8332],{},"    'StepTolerance',          1e-8);\n",[1720,8334],{},[115,8336,8338],{"id":8337},"klíčové-principy-pro-zkoušku","Klíčové principy pro zkoušku",[152,8340,8341,8352,8360,8366,8373,8380],{},[123,8342,8343,4211,8346,8348,8349],{},[38,8344,8345],{},"Maximalizace = negace",[1740,8347,7276],{}," → ",[1740,8350,8351],{},"min −f(x)",[123,8353,8354,8357,8358],{},[38,8355,8356],{},"Nepotřebná omezení"," → zadat jako ",[1740,8359,7372],{},[123,8361,8362,8365],{},[38,8363,8364],{},"x0 ovlivňuje"," které lokální minimum fmincon\u002Ffminsearch najde",[123,8367,8368,8372],{},[38,8369,8370],{},[1740,8371,7623],{}," slouží pro fine-tuning (tolerance, iterace, algoritmus)",[123,8374,8375,8379],{},[38,8376,8377],{},[1740,8378,7445],{}," je pomalejší, ale nepotřebuje gradient a hledá globální optimum",[123,8381,8382,8385,8386,8389],{},[38,8383,8384],{},"Nelineární omezení"," musí vracet ",[1740,8387,8388],{},"[c, ceq]"," — nerovnosti (c≤0) a rovnosti (ceq=0)",[115,8391,2732],{"id":2731},[152,8393,8394,8397,8400,8403],{},[123,8395,8396],{},"Čím se zabývá optimalizace?",[123,8398,8399],{},"K čemu nám slouží optimalizace?",[123,8401,8402],{},"Jaké jsou příkazy MATLABu pro optimalizaci?",[123,8404,8405],{},"Jaká jsou možná nastavení parametrů optimalizace?",[115,8407,2765],{"id":2764},[724,8409,8410],{},"Optimalizace, hledání minima, hledání maxima, příkazy optimalizace, parametry optimalizace.",[115,8412,2772,8413],{"id":2771},[207,8414,1176],{"className":8415,"dataFsResolvedFilePath":2776,"href":2777},[210],[120,8417,8418,8424],{},[123,8419,8420,8423],{},[207,8421,2785],{"className":8422,"dataFsResolvedFilePath":1562,"href":1563},[210]," — definice, kontrolní otázky, pojmy",[123,8425,8426,8430],{},[207,8427,8429],{"className":8428,"dataFsResolvedFilePath":1580,"href":1581},[210],"MATLAB Optimization Toolbox"," — kompletní MATLAB syntaxe, příklady (MathWorks docs, VUT FEEC)",[2795,8432,2797],{},{"title":641,"searchDepth":642,"depth":642,"links":8434},[8435,8436,8437,8438,8439,8453,8454,8455,8456],{"id":5220,"depth":642,"text":5221},{"id":7283,"depth":642,"text":7284},{"id":7375,"depth":642,"text":7376},{"id":7448,"depth":642,"text":7449},{"id":7494,"depth":642,"text":7495,"children":8440},[8441,8443,8445,8447,8449,8451],{"id":7498,"depth":649,"text":8442},"fmincon — nelineární optimalizace s omezeními",{"id":7824,"depth":649,"text":8444},"fminsearch — optimalizace bez omezení (Nelder-Mead)",{"id":7912,"depth":649,"text":8446},"linprog — lineární programování",{"id":8001,"depth":649,"text":8448},"intlinprog — celočíselné lineární programování (MILP)",{"id":8062,"depth":649,"text":8450},"ga — genetický algoritmus (Global Optimization Toolbox)",{"id":8164,"depth":649,"text":8452},"optimoptions — nastavení parametrů solverů",{"id":8337,"depth":642,"text":8338},{"id":2731,"depth":642,"text":2732},{"id":2764,"depth":642,"text":2765},{"id":2771,"depth":642,"text":2821},"Optimalizace je matematická disciplína, ve které hledáme minimum (resp. maximum) dané funkce f(x) na dané množině M. Tato funkce se nazývá účelová či cílová. Množina přípustných řešení bývá typicky popsána omezeními — soustavou rovnic nebo nerovnic.",{},"\u002Ftopics\u002Foptimalizace",{"title":1400,"description":8457},[1608,1610],"topics\u002Foptimalizace",[1601,1619,8464,2457,7417,7404,7445,8465],"ucelova-funkce","omezeni","AHvM3E5ql_eSnU2VAo8AAtzyssDT5aeJHSNTCu1_lN8",{"id":8468,"title":8469,"body":8470,"course":659,"courses":8624,"created":1602,"description":8625,"extension":661,"meta":8626,"navigation":664,"path":8627,"seo":8628,"sources":8629,"stem":8631,"tags":8632,"type":2835,"updated":677,"__hash__":8636},"topics\u002Ftopics\u002Fpredikce.md","Predikce a prognózování",{"type":9,"value":8471,"toc":8617},[8472,8475,8481,8485,8502,8506,8563,8567,8584,8588,8595,8600],[12,8473,8469],{"id":8474},"predikce-a-prognózování",[724,8476,8477,8478,1661],{},"Předpovídání budoucích hodnot na základě historických dat. Jedna z nejdůležitějších aplikačních oblastí v kurzu ",[207,8479,1176],{"className":8480,"href":2777,"dataFsResolvedFilePath":2776},[210],[115,8482,8484],{"id":8483},"co-se-predikuje","Co se predikuje",[120,8486,8487,8490,8493,8496,8499],{},[123,8488,8489],{},"Akciové indexy",[123,8491,8492],{},"Měnové kurzy (CZK\u002FUSD, USD\u002FEUR)",[123,8494,8495],{},"Kryptoměny",[123,8497,8498],{},"Ceny komodit (zlato, ropa, obilí)",[123,8500,8501],{},"Poptávka, prodeje, výrobní objem",[115,8503,8505],{"id":8504},"metody-predikce-v-kontextu-kurzu","Metody predikce v kontextu kurzu",[16,8507,8508,8517],{},[19,8509,8510],{},[22,8511,8512,8514],{},[25,8513,4563],{},[25,8515,8516],{},"Role v predikci",[30,8518,8519,8530,8541,8552],{},[22,8520,8521,8527],{},[35,8522,8523],{},[207,8524,5444],{"className":8525,"href":8526},[210,2857],"\u002Fwiki\u002Fumele-neuronove-site\\",[35,8528,8529],{},"Přímo se učí vzory z dat a predikují budoucí hodnoty",[22,8531,8532,8538],{},[35,8533,8534],{},[207,8535,1284],{"className":8536,"href":8537},[210,2857],"\u002Fwiki\u002Fgeneticke-algoritmy\\",[35,8539,8540],{},"Optimalizují parametry predikčního modelu nebo obchodní strategie",[22,8542,8543,8549],{},[35,8544,8545],{},[207,8546,1249],{"className":8547,"href":8548},[210,2857],"\u002Fwiki\u002Ffuzzy-logika\\",[35,8550,8551],{},"Modeluje expertní pravidla pro rozhodování o predikcích",[22,8553,8554,8560],{},[35,8555,8556],{},[207,8557,1415],{"className":8558,"href":8559},[210,2857],"\u002Fwiki\u002Fanfis\\",[35,8561,8562],{},"Hybridně kombinuje fuzzy pravidla s učením z dat",[115,8564,8566],{"id":8565},"omezení","Omezení",[120,8568,8569,8578,8581],{},[123,8570,8571,8574,8575],{},[207,8572,1297],{"className":8573,"href":1296,"dataFsResolvedFilePath":1295},[210]," ukazuje, že mnoho systémů je extrémně citlivých na počáteční podmínky → ",[38,8576,8577],{},"dlouhodobá přesná předpověď bývá prakticky nemožná",[123,8579,8580],{},"Model nedává jistotu, ale informovaný odhad",[123,8582,8583],{},"Budoucnost je nejistá — model může pracovat s více scénáři",[115,8585,8587],{"id":8586},"hurstův-exponent","Hurstův exponent",[724,8589,8590,8591,1661],{},"Rozlišuje charakter časové řady: náhodná (H = 0,5), trendová (H > 0,5), antipersistentní (H \u003C 0,5). Viz ",[207,8592,8594],{"className":8593,"href":1296,"dataFsResolvedFilePath":1295},[210],"teorie chaosu",[115,8596,2772,8597],{"id":2771},[207,8598,1176],{"className":8599,"href":2777,"dataFsResolvedFilePath":2776},[210],[120,8601,8602,8607,8612],{},[123,8603,8604],{},[207,8605,1529],{"className":8606,"href":1528,"dataFsResolvedFilePath":1527},[210],[123,8608,8609],{},[207,8610,1547],{"className":8611,"href":1546,"dataFsResolvedFilePath":1545},[210],[123,8613,8614],{},[207,8615,1297],{"className":8616,"href":1555,"dataFsResolvedFilePath":1554},[210],{"title":641,"searchDepth":642,"depth":642,"links":8618},[8619,8620,8621,8622,8623],{"id":8483,"depth":642,"text":8484},{"id":8504,"depth":642,"text":8505},{"id":8565,"depth":642,"text":8566},{"id":8586,"depth":642,"text":8587},{"id":2771,"depth":642,"text":2821},[1601],"Předpovídání budoucích hodnot na základě historických dat. Jedna z nejdůležitějších aplikačních oblastí v kurzu IpmrK.",{},"\u002Ftopics\u002Fpredikce",{"title":8469,"description":8625},[2946,5529,8630],"raw\u002Fipmrk\u002Fchaos.md","topics\u002Fpredikce",[1601,8633,8634,8635],"predikce","casove-rady","prognozovani","K7tNwF_8iNI4b3iwEgRfq_Y_VKJc5d7In2MjQU6YlLA",{"id":8638,"title":1297,"body":8639,"course":659,"courses":8954,"created":1602,"description":641,"extension":661,"meta":8955,"navigation":664,"path":8956,"seo":8957,"sources":8958,"stem":8959,"tags":8960,"type":2835,"updated":677,"__hash__":8966},"topics\u002Ftopics\u002Fteorie-chaosu.md",{"type":9,"value":8640,"toc":8937},[8641,8644,8651,8654,8657,8660,8687,8691,8702,8706,8709,8763,8767,8774,8777,8780,8784,8801,8805,8808,8846,8850,8853,8857,8860,8863,8867,8870,8872,8892,8894,8914,8916,8919,8924],[12,8642,1297],{"id":8643},"teorie-chaosu",[724,8645,8646],{},[2853,8647],{"alt":8648,"className":8649,"src":8650},"chaos-lorenz-atraktor",[210,2857],"\u002Fwiki-assets\u002Fchaos-lorenz-atraktor.jpeg",[724,8652,8653],{},"Zkoumá deterministické nelineární systémy, které se chovají nepravidelně a jsou extrémně citlivé na počáteční podmínky. Chaos ≠ náhoda — leží na spektru mezi řádem a náhodností.",[115,8655,2638],{"id":8656},"klíčové-pojmy",[198,8658,8659],{"id":1618},"Chaos",[120,8661,8662,8672,8678],{},[123,8663,8664,8665,8668,8669],{},"Systém je ",[38,8666,8667],{},"deterministický"," (má pravidla), ale dlouhodobě ",[38,8670,8671],{},"těžko předvídatelný",[123,8673,8674,8675,8677],{},"Spektrum: řád → ",[38,8676,1618],{}," → náhodnost",[123,8679,8680,8681,2866,8684],{},"Vzniká v dynamických systémech se ",[38,8682,8683],{},"zpětnou vazbou",[38,8685,8686],{},"nelinearitou",[198,8688,8690],{"id":8689},"motýlí-efekt","Motýlí efekt",[120,8692,8693,8696,8699],{},[123,8694,8695],{},"Extrémní citlivost na počáteční podmínky (Lorenz)",[123,8697,8698],{},"Malá změna na začátku → obrovský rozdíl v čase",[123,8700,8701],{},"Důsledek: dlouhodobá přesná předpověď je prakticky nemožná",[198,8703,8705],{"id":8704},"atraktory","Atraktory",[724,8707,8708],{},"Množina stavů, ke kterým systém směřuje nebo v nichž se pohybuje:",[16,8710,8711,8722],{},[19,8712,8713],{},[22,8714,8715,8717,8720],{},[25,8716,4665],{},[25,8718,8719],{},"Chování",[25,8721,5360],{},[30,8723,8724,8737,8750],{},[22,8725,8726,8731,8734],{},[35,8727,8728],{},[38,8729,8730],{},"Bodový",[35,8732,8733],{},"Ustálení v rovnováze",[35,8735,8736],{},"Kyvadlo s tlumením",[22,8738,8739,8744,8747],{},[35,8740,8741],{},[38,8742,8743],{},"Cyklický",[35,8745,8746],{},"Periodické opakování",[35,8748,8749],{},"Sezónní cykly",[22,8751,8752,8757,8760],{},[35,8753,8754],{},[38,8755,8756],{},"Chaotický (podivný)",[35,8758,8759],{},"Složitý pohyb bez přesného opakování",[35,8761,8762],{},"Strange attractor",[198,8764,8766],{"id":8765},"logistická-funkce","Logistická funkce",[724,8768,8769],{},[2853,8770],{"alt":8771,"className":8772,"src":8773},"chaos-bifurkace",[210,2857],"\u002Fwiki-assets\u002Fchaos-bifurkace.jpeg",[724,8775,8776],{},"x_{n+1} = r · xₙ · (1 − xₙ)",[724,8778,8779],{},"Jednoduchá rovnice, která podle parametru r generuje: stabilitu → oscilace → chaos. Klasická demonstrace teorie chaosu.",[198,8781,8783],{"id":8782},"fraktály","Fraktály",[120,8785,8786,8792,8795],{},[123,8787,8788,8791],{},[38,8789,8790],{},"Soběpodobné obrazce"," — podobný tvar v různých měřítkách (Mandelbrot)",[123,8793,8794],{},"Příklady: stromy, mraky, cenové grafy",[123,8796,8797,8800],{},[38,8798,8799],{},"Fraktální dimenze"," D = 2 − H — měří složitost\u002Fnepravidelnost útvaru",[198,8802,8804],{"id":8803},"hurstův-exponent-h","Hurstův exponent (H)",[724,8806,8807],{},"Analýza časových řad:",[16,8809,8810,8820],{},[19,8811,8812],{},[22,8813,8814,8817],{},[25,8815,8816],{},"Hodnota",[25,8818,8819],{},"Interpretace",[30,8821,8822,8830,8838],{},[22,8823,8824,8827],{},[35,8825,8826],{},"H = 0,5",[35,8828,8829],{},"Náhodný proces",[22,8831,8832,8835],{},[35,8833,8834],{},"H > 0,5",[35,8836,8837],{},"Persistence \u002F trendovost",[22,8839,8840,8843],{},[35,8841,8842],{},"H \u003C 0,5",[35,8844,8845],{},"Antipersistence",[198,8847,8849],{"id":8848},"elliottovy-vlny","Elliottovy vlny",[724,8851,8852],{},"Teorie tržních pohybů ve vlnách (impulsy + korekce). Ilustrace vnitřní struktury zdánlivě nepravidelného vývoje.",[115,8854,8856],{"id":8855},"zpětná-vazba","Zpětná vazba",[724,8858,8859],{},"Klíčový mechanismus chaosu: výstup systému zpětně ovlivňuje vstup → malé změny se zesilují.",[724,8861,8862],{},"V ekonomii: očekávání investorů → ceny → chování investorů → ceny.",[115,8864,8866],{"id":8865},"výskyt-chaosu","Výskyt chaosu",[724,8868,8869],{},"Matematika, fyzika, chemie, biologie, psychologie, ekonomie, finance, politika. Počasí, turbulence, finanční trhy, ekonomické cykly, sociální procesy.",[115,8871,5093],{"id":5092},[120,8873,8874,8880,8886],{},[123,8875,8876,8879],{},[207,8877,1313],{"className":8878,"dataFsResolvedFilePath":1311,"href":1312},[210]," — chaos omezuje dlouhodobou předpověditelnost",[123,8881,8882,8885],{},[207,8883,1249],{"className":8884,"dataFsResolvedFilePath":1247,"href":1248},[210]," — oba řeší nejistotu, ale jinak (neostrost vs. dynamická nepředvídatelnost)",[123,8887,8888,8891],{},[207,8889,5444],{"className":8890,"dataFsResolvedFilePath":1268,"href":1269},[210]," — mohou se učit vzory v chaotických datech",[115,8893,2732],{"id":2731},[152,8895,8896,8899,8902,8905,8908,8911],{},[123,8897,8898],{},"Co je to chaos?",[123,8900,8901],{},"Co je to atraktor?",[123,8903,8904],{},"Jaké jsou typy atraktoru?",[123,8906,8907],{},"Co je to fraktál?",[123,8909,8910],{},"Co jsou to Elliottovy vlny?",[123,8912,8913],{},"Kdo je zakladatelem teorie fraktálů?",[115,8915,2765],{"id":2764},[724,8917,8918],{},"Chaos, nahodilost a řád, rovnováha, atraktor, fraktál, soběpodobnost, soběpříbuznost.",[115,8920,2772,8921],{"id":2771},[207,8922,1176],{"className":8923,"dataFsResolvedFilePath":2776,"href":2777},[210],[120,8925,8926,8932],{},[123,8927,8928],{},[207,8929,8931],{"className":8930,"dataFsResolvedFilePath":1554,"href":1555},[210],"Teorie chaosu — shrnutí přednášky",[123,8933,8934,5172],{},[207,8935,2785],{"className":8936,"dataFsResolvedFilePath":1562,"href":1563},[210],{"title":641,"searchDepth":642,"depth":642,"links":8938},[8939,8948,8949,8950,8951,8952,8953],{"id":8656,"depth":642,"text":2638,"children":8940},[8941,8942,8943,8944,8945,8946,8947],{"id":1618,"depth":649,"text":8659},{"id":8689,"depth":649,"text":8690},{"id":8704,"depth":649,"text":8705},{"id":8765,"depth":649,"text":8766},{"id":8782,"depth":649,"text":8783},{"id":8803,"depth":649,"text":8804},{"id":8848,"depth":649,"text":8849},{"id":8855,"depth":642,"text":8856},{"id":8865,"depth":642,"text":8866},{"id":5092,"depth":642,"text":5093},{"id":2731,"depth":642,"text":2732},{"id":2764,"depth":642,"text":2765},{"id":2771,"depth":642,"text":2821},[1601],{},"\u002Ftopics\u002Fteorie-chaosu",{"title":1297,"description":641},[8630,1608],"topics\u002Fteorie-chaosu",[1601,1618,8704,8961,8962,8963,8964,8965],"fraktaly","hurst","motyli-efekt","logisticka-funkce","lorenz","9_KE3En_XZkN73ydbuFmiWlnjt-zr6FQ4aFJizQUcmg",{"id":8968,"title":1270,"body":8969,"course":659,"courses":9313,"created":1602,"description":641,"extension":661,"meta":9314,"navigation":664,"path":9315,"seo":9316,"sources":9317,"stem":9318,"tags":9319,"type":2835,"updated":677,"__hash__":9323},"topics\u002Ftopics\u002Fumele-neuronove-site.md",{"type":9,"value":8970,"toc":9296},[8971,8974,8981,8984,8988,8992,8999,9019,9023,9084,9088,9114,9118,9126,9133,9150,9154,9171,9175,9189,9191,9217,9219,9239,9241,9264,9266,9269,9274],[12,8972,1270],{"id":8973},"umělé-neuronové-sítě",[724,8975,8976],{},[2853,8977],{"alt":8978,"className":8979,"src":8980},"nn-vicevrstva-sit",[210,2857],"\u002Fwiki-assets\u002Fnn-vicevrstva-sit.jpeg",[724,8982,8983],{},"Výpočetní model inspirovaný biologickým nervovým systémem. Soustava propojených neuronů, které se z dat učí rozpoznávat vzory, klasifikovat a predikovat.",[115,8985,8987],{"id":8986},"stavební-kameny","Stavební kameny",[198,8989,8991],{"id":8990},"perceptron-umělý-neuron","Perceptron (umělý neuron)",[724,8993,8994],{},[2853,8995],{"alt":8996,"className":8997,"src":8998},"nn-perceptron",[210,2857],"\u002Fwiki-assets\u002Fnn-perceptron.jpeg",[120,9000,9001,9004,9007,9013],{},[123,9002,9003],{},"Vstupy i₁..iₙ × váhy w₁..wₙ → vážený součet + bias → aktivační funkce → výstup",[123,9005,9006],{},"Matematicky: a = Σ(iⱼ·wⱼ) + b, výstup m = f(a)",[123,9008,9009,9012],{},[38,9010,9011],{},"Váhy"," nesou naučenou znalost (kladné posilují, záporné tlumí)",[123,9014,9015,9018],{},[38,9016,9017],{},"Bias"," posouvá rozhodovací hranici",[198,9020,9022],{"id":9021},"aktivační-funkce","Aktivační funkce",[16,9024,9025,9040],{},[19,9026,9027],{},[22,9028,9029,9032,9035,9037],{},[25,9030,9031],{},"Funkce",[25,9033,9034],{},"Vzorec",[25,9036,5046],{},[25,9038,9039],{},"Použití",[30,9041,9042,9056,9070],{},[22,9043,9044,9047,9050,9053],{},[35,9045,9046],{},"Lineární",[35,9048,9049],{},"m = a",[35,9051,9052],{},"ℝ",[35,9054,9055],{},"Jednoduchý, bez nelinearity",[22,9057,9058,9061,9064,9067],{},[35,9059,9060],{},"Logistický sigmoid",[35,9062,9063],{},"m = 1\u002F(1+e⁻ᵃ)",[35,9065,9066],{},"(0, 1)",[35,9068,9069],{},"Pravděpodobnost, binární klasifikace",[22,9071,9072,9075,9078,9081],{},[35,9073,9074],{},"Hyperbolický tangens",[35,9076,9077],{},"m = tanh(a)",[35,9079,9080],{},"(−1, 1)",[35,9082,9083],{},"Kladné i záporné aktivace",[198,9085,9087],{"id":9086},"vícevrstvá-síť","Vícevrstvá síť",[120,9089,9090,9096,9102,9108],{},[123,9091,9092,9095],{},[38,9093,9094],{},"Vstupní vrstva"," — přijímá data",[123,9097,9098,9101],{},[38,9099,9100],{},"Skryté vrstvy"," — vytvářejí vnitřní reprezentace, zachycují nelinearitu",[123,9103,9104,9107],{},[38,9105,9106],{},"Výstupní vrstva"," — konečné rozhodnutí nebo predikce",[123,9109,9110,9113],{},[38,9111,9112],{},"Deep learning"," — mnoho vrstev a parametrů, pro složité úlohy s velkým objemem dat",[115,9115,9117],{"id":9116},"učení","Učení",[198,9119,9120],{"id":3059},[207,9121,9125],{"className":9122,"dataFsResolvedFilePath":9123,"href":9124},[210],"topics\u002Fbackpropagation.md","\u002Fwiki\u002Fbackpropagation","Backpropagation",[724,9127,9128],{},[2853,9129],{"alt":9130,"className":9131,"src":9132},"nn-backpropagation",[210,2857],"\u002Fwiki-assets\u002Fnn-backpropagation.jpeg",[152,9134,9135,9138,9141,9144,9147],{},[123,9136,9137],{},"Dopředný průchod — výpočet výstupu",[123,9139,9140],{},"Výpočet chyby (e = cíl − výstup)",[123,9142,9143],{},"Zpětné šíření chyby přes vrstvy",[123,9145,9146],{},"Úprava vah ve směru snížení chyby",[123,9148,9149],{},"Opakování (iterativní proces)",[198,9151,9153],{"id":9152},"praktický-postup","Praktický postup",[152,9155,9156,9159,9162,9165,9168],{},[123,9157,9158],{},"Připravit data (matice vstupů a výstupů)",[123,9160,9161],{},"Zvolit architekturu (počet vrstev, neuronů, aktivační funkce)",[123,9163,9164],{},"Rozdělit data na trénovací\u002Ftestovací (např. 75\u002F25 %)",[123,9166,9167],{},"Trénovat a sledovat průběh chyby",[123,9169,9170],{},"Kritéria ukončení: min chyba, max iterací, max čas",[198,9172,9174],{"id":9173},"kompromis-jednoduchost-vs-složitost","Kompromis jednoduchost vs. složitost",[120,9176,9177,9183],{},[123,9178,9179,9182],{},[38,9180,9181],{},"Podučený model"," — příliš jednoduchý, vysoká chyba",[123,9184,9185,9188],{},[38,9186,9187],{},"Přeučený model"," — naučí se i šum, nefunguje na nových datech",[115,9190,5348],{"id":5347},[120,9192,9193,9196,9199,9202,9205,9208,9214],{},[123,9194,9195],{},"Hodnocení bonity klienta (scoring)",[123,9197,9198],{},"Oceňování (nemovitosti, auta, produkty)",[123,9200,9201],{},"Vyhodnocení investic a rizika",[123,9203,9204],{},"Detekce podvodů (praní peněz, daňové anomálie)",[123,9206,9207],{},"Rozpoznávání obrazu, písma, zvuku, překlad",[123,9209,9210,9213],{},[207,9211,1313],{"className":9212,"dataFsResolvedFilePath":1311,"href":1312},[210]," časových řad (akcie, měny, komodity)",[123,9215,9216],{},"Diagnostika nemocí, autonomní systémy",[115,9218,5093],{"id":5092},[120,9220,9221,9227,9233],{},[123,9222,9223,9226],{},[207,9224,1415],{"className":9225,"dataFsResolvedFilePath":1413,"href":1414},[210]," — hybridní systém: fuzzy struktura + učení neuronové sítě",[123,9228,9229,9232],{},[207,9230,1249],{"className":9231,"dataFsResolvedFilePath":1247,"href":1248},[210]," — partner v ANFIS",[123,9234,9235,9238],{},[207,9236,1284],{"className":9237,"dataFsResolvedFilePath":1282,"href":1283},[210]," — mohou optimalizovat architekturu sítě",[115,9240,2732],{"id":2731},[152,9242,9243,9246,9249,9252,9255,9258,9261],{},[123,9244,9245],{},"Popište metodu a vysvětlete princip neuronových sítí.",[123,9247,9248],{},"Popište realizaci a výpočet neuronových sítí na počítači.",[123,9250,9251],{},"Jak lze využít neuronových sítí v praxi?",[123,9253,9254],{},"Kdy je vhodné použít neuronových sítí?",[123,9256,9257],{},"Jaký je správný postup kroků při výpočtu pomocí neuronových sítí?",[123,9259,9260],{},"Jaké vrstvy mají neuronové sítě?",[123,9262,9263],{},"Jaké jsou typy přenosových funkcí?",[115,9265,2765],{"id":2764},[724,9267,9268],{},"Neuronová síť, učení, testování, vstupní matice, přenosová funkce.",[115,9270,2772,9271],{"id":2771},[207,9272,1176],{"className":9273,"dataFsResolvedFilePath":2776,"href":2777},[210],[120,9275,9276,9281,9286,9291],{},[123,9277,9278],{},[207,9279,1511],{"className":9280,"dataFsResolvedFilePath":1509,"href":1510},[210],[123,9282,9283],{},[207,9284,1520],{"className":9285,"dataFsResolvedFilePath":1518,"href":1519},[210],[123,9287,9288],{},[207,9289,1529],{"className":9290,"dataFsResolvedFilePath":1527,"href":1528},[210],[123,9292,9293,5172],{},[207,9294,2785],{"className":9295,"dataFsResolvedFilePath":1562,"href":1563},[210],{"title":641,"searchDepth":642,"depth":642,"links":9297},[9298,9303,9308,9309,9310,9311,9312],{"id":8986,"depth":642,"text":8987,"children":9299},[9300,9301,9302],{"id":8990,"depth":649,"text":8991},{"id":9021,"depth":649,"text":9022},{"id":9086,"depth":649,"text":9087},{"id":9116,"depth":642,"text":9117,"children":9304},[9305,9306,9307],{"id":3059,"depth":649,"text":9125},{"id":9152,"depth":649,"text":9153},{"id":9173,"depth":649,"text":9174},{"id":5347,"depth":642,"text":5348},{"id":5092,"depth":642,"text":5093},{"id":2731,"depth":642,"text":2732},{"id":2764,"depth":642,"text":2765},{"id":2771,"depth":642,"text":2821},[1601],{},"\u002Ftopics\u002Fumele-neuronove-site",{"title":1270,"description":641},[3055,3056,2946,1608],"topics\u002Fumele-neuronove-site",[1601,1615,9320,3059,9321,9322,8633],"perceptron","deep-learning","klasifikace","2MvJHrE1Kihv1j7VlanYSB_CCyk_IdCCqYQ_wceZWs4",[9325,9327,9329,9334,9338],{"slug":1617,"path":1384,"title":1385,"snippet":9326},"… Souvisí s: genetické algoritmy (podmnožina EA), optimalizace, \u003C\u003Cdatamining>>. ## Základní princip - Hledáme optimum **účelové funkce** za daných **omezujících podmí …",{"slug":1601,"path":2777,"title":1150,"snippet":9328},"… -algoritmy|Genetické algoritmy]] + aplikace MATLAB 9. Teorie chaosu 10. \u003C\u003Cdatamining>> 11. Predikce, kapitálový trh 12. Řízení výroby a řízení rizik 13. Rozhodován …",{"slug":9330,"path":9331,"title":9332,"snippet":9333},"ipmrk-co-studovat","\u002Fwiki\u002Fipmrk-co-studovat","IpmrK — Co studovat ke zkoušce","… malizace]] | ❌ Mezera | Jen shrnutí z knihy. Chybí MATLAB příkazy, příklady úloh. | | 7 | \u003C\u003Cdatamining>> | ❌ Mezera | Jen shrnutí z knihy. Chybí Witness Miner, příklady, techniky. | ## Co dohle …",{"slug":9335,"path":1563,"title":9336,"snippet":9337},"ipmrk-kniha","IpmrK Kniha — Pokročilé metody analýz a modelování","… nová témata**: evoluční algoritmy, optimalizaci a \u003C\u003Cdatamining>>. ## Pokryté kapitoly ### 1. Fuzzy logika (kap. 2) - Teorie L. Zadeha — …",{"slug":1619,"path":1399,"title":1400,"snippet":9339},"… : genetické algoritmy, evoluční algoritmy, \u003C\u003Cdatamining>>. ## Základní pojmy Každá optimalizační úloha obsahuje tři složky: - **Stavové (rozhodo …",[9341,9343,9346],{"slug":9342,"title":1591,"path":1590,"sharedTags":2503},"ipmrk-datamining",{"slug":9344,"title":9345,"path":1546,"sharedTags":642},"ipmrk-ga-vyuziti","Genetické algoritmy — praktické aplikace",{"slug":9335,"title":9336,"path":1563,"sharedTags":642},1777154952471]