Data-Driven Optimization-Yinyu Ye

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1、DistributionallyRobustOptimization(DRO)OnlineLinearProgramming(OLP)LeastSquareswithNonconvexRegularization(LSNR)AlternatingDirectionMethodofMultipliers(ADMM)Data-DrivenOptimizationYinyuYeK.T.LiChairProfessorofEngineeringDepartmentofManagementScienceandEngineeringStanfordUniversityJune,2014Yi

2、nyuYeJune2014DistributionallyRobustOptimization(DRO)OnlineLinearProgramming(OLP)LeastSquareswithNonconvexRegularization(LSNR)AlternatingDirectionMethodofMultipliers(ADMM)OutlineWepresentseveraloptimizationmodelsand/orcomputationalalgorithmsdealingwithuncertain,dynamic/online,structuredand/or

3、massivelydistributeddata:DistributionallyRobustOptimization(datauncertainty)OnlineLinearProgramming(datadynamics)LeastSquareswithNonconvexRegularization(datastructure)TheADMMMethodwithMultipleBlocks(datasize)YinyuYeJune2014DistributionallyRobustOptimization(DRO)OnlineLinearProgramming(OL

4、P)LeastSquareswithNonconvexRegularization(LSNR)AlternatingDirectionMethodofMultipliers(ADMM)MathematicalOptimizationClassicmathematicaloptimizationconsiders:maximizex∈Dh(x)Sinceh(x)maybepartiallydecidedbyotherinputdata,sayξ,weactuallymaximizex∈Dh(x,E[ξ])YinyuYeJune2014DistributionallyRobustO

5、ptimization(DRO)OnlineLinearProgramming(OLP)LeastSquareswithNonconvexRegularization(LSNR)AlternatingDirectionMethodofMultipliers(ADMM)DistributionallyRobustOptimization(DRO)Thismaybetoosimplistic,peopleconsiderastochasticoptimizationproblemasfollows:maximizex∈DEFξ[h(x,ξ)](1)wherexisthedecisi

6、onvariablevectorwithfeasibleregionD,ξisarandomparametervectorwithdensityordistributionFξ.Pros:Inmanycases,theexpectedvalueisagoodmeasureofperformance.Cons:Onehastoknowtheexactdistributionofξtoperformthestochasticoptimization.Deviantfromtheassumeddistributionmayresultinsub-optimalsolutions.

7、YinyuYeJune2014DistributionallyRobustOptimization(DRO)OnlineLinearProgramming(OLP)LeastSquareswithNonconvexRegularization(LSNR)AlternatingDirectionMethodofMultipliers(ADMM)RobustOptimizationInordertoovercomethelackofknowledgeonthedistribution,peopl