Inthispaper,LCPisconvertedtoanequivalentnonsmoothnonlinearequationsystemH(x,y)=0byusingthefamousNCPfunction-Fischer-Burmeisterfunction.NotethatsomeequationsinH(x,y)=0arenonsmoothandnonlinearhencedifficulttosolvewhiletheothersarelinearhenceeasytosolve.ThenwefurtherconvertthenonlinearequationsystemH(x,y)=0toanoptimizationproblemwithlinearequalityconstraints.AfterthatwestudytheconditionsunderwhichtheK-TpointsoftheoptimizationproblemarethesolutionsoftheoriginalLCPandproposeamethodtosolvetheoptimizationproblem.Inthisalgorithm,thesearchdirectionisobtainedbysolvingastrictconvexprogrammingateachiterativepoint,However,ouralgorithmisessentiallydifferentfromtraditionalSQPmethod.Theglobalconvergenceofthemethodisprovedundermildconditions.Inaddition,wecanprovethatthealgorithmisconvergentsuperlinearlyundertheconditions:MisP0matrixandthelimitpointisastrictcomplementaritysolutionofLCP.Preliminarynumericalexperimentsarereportedwiththismethod.
