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基于块分裂求解线性互补问题的新模系同步多分裂方法（英文）.docx

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基于块分裂求解线性互补问题的新模系同步多分裂方法（英文） NewMonolithicSynchronizedMulti-SplittingMethodforSolvingLinearComplementarityProblemsbasedonBlockSplitting Abstract Inthispaper,weintroduceanewmonolithicsynchronizedmulti-splittingmethod,whichisappliedtosolvelinearcomplementarityproblemsthatarebasedonblocksplitting.Theproposedmethodhastheadvantageofprovidingafastconvergencerate,anditcanhandlelarge-scalelinearcomplementarityproblemsefficiently.Inaddition,itisimplementedinaparalleldistributedcomputingenvironment,whichfurtherenhancesitscomputationalefficiency.Numericalexperimentsareconductedtovalidateourclaims,andtheresultsshowthattheproposedmethodoutperformsexistingmethodsintermsofconvergencespeedandaccuracy. Introduction Linearcomplementarityproblems(LCPs)areubiquitousinvariousfields,suchaseconomics,engineering,andphysics.LCPsareaclassofnonlinearproblemsthatinvolvefindinganon-negativesolutionsubjecttolinearconstraints.ManyalgorithmshavebeendevelopedtosolveLCPs,includingtheLemke-Howsonalgorithm,thePathfollowingalgorithm,theProjectivemethodalgorithm,andtheProximalpointalgorithm.However,thesealgorithmssufferfrompoorconvergencepropertiesandhighcomputationalcostwhenappliedtolarge-scaleproblems. Recently,blocksplittingtechniqueshavebeenproposedtoimprovetheconvergencerateandcomputationalefficiencyofLCPalgorithms.Ouraimistoextendtheexistingblocksplittingtechniquestodevelopanewmonolithicsynchronizedmulti-splittingmethodthatcansolvelarge-scaleLCPsefficiently.Theproposedmethodisimplementedusingaparalleldistributedcomputingenvironment,whichfurtherenhancesitscomputationalefficiency. Methodology Theproposedmethodisbasedonblocksplitting,wheretheproblemissplitintoseveralsub-problems.Weuseamonolithicsynchronizedapproach,whereallthesub-problemsaresolvedsimultaneouslyusingasingleiterativeprocess.Thisapproachensuresglobalconvergence,anditavoidstheneedforanyparametertuning. Theproposedmethodusesamulti-splittingapproach,whereeachsub-problemissplitintomultiplesmallersub-problems.Thisapproachfurtherimprovestheco