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首页 最优化理论与方法课件(英文版-南京大学)最优化-quiz2-ans

最优化理论与方法课件(英文版-南京大学)最优化-quiz2-ans.doc

最优化理论与方法课件(英文版-南京大学)最优化-quiz2-a…

chuanyinworkday
2018-09-08 0人阅读 举报 0 0 暂无简介

简介:本文档为《最优化理论与方法课件(英文版-南京大学)最优化-quiz2-ansdoc》,可适用于高等教育领域

OptimizationTheoryandMethodFallQuiz#QConsidertheproblem()Determinethesolutiontothisproblem()Formulatethedual,anddeterminewhetheritslocalsolutiongivestheLagrangemultipliersattheoptimalsolutionSolObviously,theoptimalsolutionisTheLagrangianfunctionisTheKKTconditionsareasbelow:Attheoptimalsolution,theLagrangemultiplierInthiscase,thedualfunctionisforFromThusthedualfunctiontakestheformforThedualproblemisthereforeItiseasytoseethatthesolutionisHence,thelocalsolutionofthedualproblemdoesgivetheLagrangemultipliersattheoptimalsolutionQLetbeasolutiontotheproblemwhereeachisdifferentiableThenthereexistsanumbersuchthatSolLetandbetheLagrangianmultipliersassociatedwithconstraintsandrespectivelyThen,theLagrangianfunctionofthisproblemisSinceistheoptimalsolutionoftheconcernedproblem,itsatisfiestheKKTconditionsThatis,ThefirstequationmeansThen,accordingtothelastcomplementaryconditions,thereexistsanumbersuchthatQConsidertheproblemSupposethatthelogarithmicbarriermethodisusedtosolvethisproblemWhatisWhatisWhatisWhatisSolThelogarithmicbarrierfunctionisThefirstorderconditionforisIt’sobviousthatSubstitutingthisinthefirstequationabove,wehavethatiswhen,when,,QGluecoisplanningtointroduceanewproductinthreedifferentregionsPresentestimatesarethattheproductwillsellwellineachregionwithrespectiveprobabilities,,andThefirmhasavailabletwotopsalesrepresentativesthatitcansendtoanyofthethreeregionsTheestimatedprobabilitiesthattheproductwillsellwellineachregionwhen,,oradditionalsalesrepresentativesaresenttoaregionaregiveninthefollowingtableIfGluecowantstomaximizetheprobabilitythatitsnewproductwillsellwellinallthreeregions,whereshouldthecompanyassignitssalesrepresentativesYoumayassumethatsalesinthethreeregionsareindependentNoofadditionalSalesRepresentativesProbabilityofSellingWellRegionRegionRegionSolLetThen,wherePAGEunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknownunknown

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