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1、XEpsjnqj9I/I/SI0ZLUOJsXgUOUBUIJOJUIpUBUOpB0IUnUJUIO3:JO闻N：QI呻pius****SuiuiuibjSojjJEauiqjojpoqppvjuiod-jouajuj(Bnp-iBiuudpucpoqpj[jaujcguopcziuipdoXAOJOJ屮OM
2、BUIJBarrierMethodandPrimal-dualInterior-pointMethodforLinearProgrammingSchoolofInformationScienceandEngineer
3、ing,ShandongUniversity,P.R.China,250100*@maii.sdu.edu.cnAbstract：Interior-pointmethods(IMP)forsolvingconvexoptimizationproblemsthatincludeinequalityconstraints.ThemostattractivefeaturesofIMPareitsspeedofconvergenceanditsrobustcapabilityofhandlingequalityandinequalit
4、yconstraints;makingitselfapracticaltoolforsolvinglarge-scaleoptimizationproblems.Inthispaper,twokindsofinterior-pointmethods—bairiermethodandprimal-dualinterior-pointmethod,arediscussed.AndComparisonofthesetwomethodsisgiven、basedonsolvingthestandardLP.Keywords:Inter
5、ior-pointmethod,BaiTiermethod,Primal-dualinterior-pointmethod,LP.1IntroductionTheinterior-pointmethodisalmostusedtosolveconvexoptimizationproblemsthatincludeinequalityconstraints.Interior-pointmethodssolvetheproblem(ortheKKTconditions)byapplyingNewton'smethodtoasequ
6、enceofequalityconstrainedproblems,ortoasequenceofmodifiedversionsoftheKKTconditions・Wecanviewinterior-pointmethodsasanotherlevelinthehierarchyofconvexoptimizationalgorithms.Linearequalityconstrainedquadraticproblemsarethesimplest.FortheseproblemstheKKTconditionsarea
7、setoflinearequations,whichcanbesolvedanalytically.Newton，smethodisthenextlevelinthehierarchy.WecanthinkofNewton'smethodasatechniqueforsolvingalinearequalityconstrainedoptimizationproblem,withtwicedifferentiableobjective,byreducingittoasequenceoflinearequalityconstra
8、inedquadraticproblems.Interior-pointmethodsformthenextlevelinthehierarchy:Theysolveanoptimizationproblemwithlinearequalityandinequalityconstraintsbyreducingittoasequenceoflinearequalityconstrainedproblems.2Theorybasisinthischapterwcdiscussinterior-pointmethodsforsol
9、vingconvexoptimizationproblemsthatincludeinequalityconstraints,minimize/o(x)s.t.fiM<0,i=1,2•••m(2.1)Ax=bwhere...fm:R"tRarcconvexandtwiceco
