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一个求解退化约束优化问题全局和超线性收敛的可行SQP算法(英文).docx

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一个求解退化约束优化问题全局和超线性收敛的可行SQP算法(英文) Title:AFeasibleSQPAlgorithmforSolvingDegenerateConstrainedOptimizationProblemswithGlobalandSuperlinearConvergence Abstract: Degenerateconstrainedoptimizationproblemsoccurfrequentlyinvariousdomains,posingsignificantchallengesforoptimizationalgorithmsintermsofbothfeasibilityandconvergence.Inthispaper,weproposeanovelSequentialQuadraticProgramming(SQP)algorithmthataddressesthesechallengesbyincorporatingbothglobalandsuperlinearconvergenceproperties.Thealgorithmaimstofindafeasiblesolutionwhilealsoguaranteeingconvergencetoanoptimalsolutionefficiently.Theeffectivenessandrobustnessofthealgorithmaredemonstratedthroughcomprehensivenumericalexperimentsondegenerateoptimizationproblems. 1.Introduction: Constrainedoptimizationproblemswithdegenerateconstraintsareencounteredinawiderangeofapplications,suchasengineering,economics,andfinance.Theseproblemsinvolveconstraintsthatmaylosetheiractivestatusatcertainpointsinthesearchspace,leadingtodifficultiesinfindingfeasiblesolutions.Additionally,achievingconvergencetotheglobaloptimalsolutioninthepresenceofdegenerateconstraintsremainsamajorchallenge.TheobjectiveofthispaperistoproposeafeasibleSQPalgorithmthatovercomesthesechallengesandensuresbothglobalandsuperlinearconvergence. 2.LiteratureReview: Inrecentyears,severaloptimizationalgorithmshavebeendevelopedtotackledegenerateconstrainedoptimizationproblems.However,mostofthesealgorithmsfocusonlocalconvergenceandstruggletohandledegenerateconstraintseffectively.Somenotablemethodsincludeinterior-pointalgorithms,activesetmethods,andpenaltymethods.Whilethesemethodshavemadesignificantcontributions,theyoftensufferfromconvergenceissuesandmayfailtoprovidefeasiblesolutions. 3.Methodology: Ourproposedalgorithmcombineselementsfrombothinterior-pointmethodsandSQPmethodstohandledegenerateconstraintseffectively.ThekeyideaistomodifythestandardSQPalgorithmtoincorporateglobalconvergencepropertiesbydynamicallyadjustingtheinterior-pointparameterduringtheoptimizationprocess.Thismodif