一类分布鲁棒二次规划问题

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1、万方数据大连理工大学硕士学位论文AclassofdistributionallyrobustquadraticprogrammingproblemsAbstractDistributionallyRobustOptimizationProblemsconsidertheportfolio’SnondeterminacyinthebasicofrobustOptimizationProblems．AsanextentiontoMarkovitz’Sexpectation·variationmodel，thispaperdiscussac

2、lassofdistributionallyrobustquadraticprogrammingproblems．Withthehelpofdualitytheory，weshowthatthisclassofproblemsareequivalenttoaclassoftractableconvexquadraticSDPprogrammingproblems．Numericalresultsarereportedtoshowthatthesolutionsobtainedbythedistributionallyrobustopt

3、imizationmodel3xereasonable．Themainresultsofthisdissertationaresummarizedasfollows：1．Chapter1firstgivesabackgroundsurveyaboutthedistributionallyrobustoptimizationandtheMarkowitzportfoliomodel，includingitsbackgroundanddevelopment．Thenweproposeaclassofdistributionallyrobu

4、stquadraticprogrammingproblems，whichwillbestudiedinthisthesis．2．InChapter2，weintroducesomepreliminariesaboutmatricesandprobabilityaswellasthedualitytheory，whichwillbeusedinthisthesis．3．InChapter3，wedemonstratethattheproblemscorrespondingtothoseuncertaintystructuresCanbe

5、turnedtoconvexquadraticprograms，andthisresultisobtainedbyusingtheLagrangedualitymethodtodealwithboththeobjectivefunctionandtheconstraintfunction．4．InChapter4，wemakenumericaltestsbyusingtheMatlabtoolboxYALMIPtoverifytheperformanceoftheproposedmodel．Afterthatweanalyzenume

6、ricalexampleandfindthattherobustoptimizationmodelhasadvantagesoverthenormaldistributionportfoliomodelinavoidingrisk．Then：wecomparethemodelonlyintheriskconstraintwiththismodel：wefindthismode】hasbetterrobustness．KeyWords：Distributionallyrobustoptimization；Minimumvariance；

7、Lagrangedual；ConvexQuadraticproblemIII万方数据一类分布鲁棒二次规划问题IV万方数据大连理工大学硕士学位论文目录摘要⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．IAbstract⋯⋯．．．．．．⋯⋯⋯．⋯⋯⋯．．．⋯⋯．．．．．．．．⋯⋯．．．．．．．．．．．．．⋯⋯．⋯．．III1引言⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．11．1均值方差模型的产生与发展⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯11．2鲁棒优化⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．21．3分布鲁棒优化

8、问题的背景⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯21．4本文的主要工作⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯42预备知识⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．52．1矩阵基础知识⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯