资源描述：
《A Second-Order Method for the .pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、JOURNALOFOPTIMIZATIONTHEORYANDAPPLICATIONS:Vol.26,No.4,DECEMBER1978ASecond-OrderMethodfortheGeneralNonlinearProgrammingProblem1H,MUKAI2ANDE.POLAK3CommunicatedbyD.Q.MayneAbstract.Thispaperpresentsamultiplier-typemethodfornonlinearprogrammingproblemswithb
2、othequalityandinequalityconstraints.Slackvariablesareusedfortheinequalities.Thepenaltycoefficientisadjustedautomatically,andthemethodconvergesquadraticallytopointssatisfyingsecond-orderconditions.KeyWords.Multipliermethod,quadraticconvergence,nonlinearp
3、rogramming,slackvariables.1.IntroductionAlthoughsimilarideaswereusedinthestudyofsecond-ordercondi-tionsasfarbackasthe1930's[see,e.g.,Hestenes(Ref.1)],primal-dualmethods,intheircurrentform,arederivedfrommorerecentproposalsbyHestenes(Ref.2),Powell(Ref.3),
4、andsomewhatlaterHaarhoffandBuys(Ref.4).Specifically,inthecaseofproblemsoftheformmin{f(x)lg(x)=0},theydependonaninterestingpropertyoftheLagrangianf(x)+cllg(x)ll2+(~,g(x))oftheequivalentproblemminK/(x)+cllg(x)llZlg(x)=0}.1Theworkofthefirstauthorwassupport
5、edbyNSFRANNandJSEPContractNo.F44620-71-C-0087;theworkofthesecondauthorwassupportedbytheNationalScienceFoundationGrantNo.ENG73-08214A01andUSArmyResearchOfficeDurhamContractNo.DAHC04-73-C-0025.2AssistantProfessor,DepartmentofSystemsScienceandMathematics,W
6、ashingtonUni-versity,St.Louis,Missouri.3Professor,DepartmentofElectricalEngineeringandComputerSciences,andtheElectronicsResearchLaboratory,UniversityofCalifornia,Berkeley,Califorinia.5150022-3239/78/1200-0515505.00/0©1978PlenumPublishingCorporation516JO
7、TA:VOL.26,NO.4,DECEMBER1978Namely,forhsuitablychosenandclargeenough,thelocalminimizersofthisLagrangianarealsolocalminimizersoftheoriginalproblem.Becauseprimal-dualmethodsreduceanequalityconstrainedminimizationproblemtoanunconstrainedone,somewhatlikepena
8、ltyfunctionmethods,butwithouttheaccompanyingill-conditioningofordinarypenaltyfunctionmethods,theyhaveattractedagreatdealofattention[seeBuys(Ref.5),PolyakandTret'yakov(Ref.6),Mieleetal.(Refs.7-10),TripathiandNarendra(Ref.11),Rupp(
