minmaxmin规划的凝聚同伦方法及其在数据挖掘中的应用

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1、大连理工大学博士学位论文min-max-min规划的凝聚同伦方法及其在数据挖掘中的应用姓名：熊慧娟申请学位级别：博士专业：计算数学指导教师：于波20090901min，max-rain规划的凝聚同伦方法及其在数据挖掘中的应用AggregateHomotowMethodsforMin—max-rainProgrammingwithApplicationsinDataMiningAbstractMin—max-rainprogrammingisakindofimportantnonsmoothproblemthatappearsinvariousfieldssuchase

2、ngineeringoptimizationdesign：circuitdesignanddatamining．Thethesisisbasedontheexistingaggregatehomotopymethod，itconsistsofthefollowingsections：InChapter1．min-max-minprogrammingproblemwithitsapplicationgroundist01’一mulated，andsomeresultsonrelatedtheoryandalgorithmsarerecalled．InChapter2，b

3、ygivingatruncatedaggregatestrategy,allefficienttruncateaggregatemethodfornumericallytracingaggregatehomotopypathisintroduced．Atevery．iteration，onlyapartofcomponentfunctionsareusedtomakeaggregatesmoothingapproximation．whoseindexsetisupdatedadaptivelywithatruncatedaggregatecriterion．Thecr

4、ite-rionconcernsonlywithcomputationofcomponentfunctionsvalue，nottheirgradientsorHessian．Basedonthecriterion，theconvergenceofthetruncatedaggregatehomotopymethodandlocallyquadraticconvergenceofthecorrectoriterationsat,every．steparedis-cussed．InChapter3，usingtwiceaggregatefunction，anewaggr

5、egatedeformationhomotopymethodisestablishedtosolvemin-max-minprogramming．Comparedtoaggregatehomo-towmethod，thenewmethoddoesn’trequiretheweaknormalconeconditionanddoesn’trequireaninteriorinitialpoint．InChapter4：basedonthewellknowndiscretizedconsistentapproximatestrate93jasemi-infiniterai

6、n—max-minprogrammingisapproximatedbyfinitemin-max-minproblems．It‘sproventhatanE-substationarypointCanbeobtainedbysolvingsomedenseenoughrain-max-rainprogrammingwithtruncatedaggregatehomotopymethod．InChapter5，asemi-infinitemin-max-minproblemisreformulatedintoaspecialbi—levelproblem．Undera

7、nassumptionthatthelowerlevelproblemisastrictlyconvexproblem，afirst-orderoptimaliWconditionoftheoriginalproMemisgiven．Anaggregatehomotopyisestablishedforsolvingtheproblem．It’sproventhatthchomotowdeterminesasmoothpath．whichapproachingtoasolutionofagenerahzedKKTpointoftheoriginalp