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1、(NLP)NLPKKTNLPKKTKKTKKT1.KKTKKTLagrangeLagrange2.LagrangeLagrangeKKTAbstractTheconstrainednonlinearprogrammingproblems(NLP)isaveryimportantcompo-nentpartinoperationsresearch,Ithaswideapplicationinnaturalscience,engineeringandeconomics.ThetypicalmethodforsolvingNLPhavefeasibledire
2、ctionmethod,penaltyfunctionmethod,multipliermethod,sequentialquadraticprogrammingandsoon.Inrecentyears,themethodthatalocalminimumofNLPisobtainedbysolvingKKT-systemsforNLPbecomesoneoftheefficientnumericalmethodsforNLP.ThemainideaofthemethodistoreformulatetheKKT-conditionsforNLPassmo
3、othnonlinearequations,thenaKKT-pointforNLPisobtainedbyusingclassicalnumericalmethodsfortheproblem.ThemethodsinthisthesisaKKT-pointisobtained,butthedifferencetrainofthoughttosolvetheproblem.Thespecificcontentsareasfollows:1.Thefirstweconstructanewauxiliaryfunctioncontainingparameter,
4、usingthegoodpropertysofthisfunction.Theconstraintoptimizationproblemswithinequalityconstraintsintoequivalentconversion.ThisconversionnotonlyensuretheKKT-conditionofthenewproblemsandtheKKT-conditionoftheoriginalproblemswiththesolution,butalsotheintroductionofparametersmaketheLagra
5、ngefunctionofthenewproblemswithapenaltyfunction.Usingthischaracteristic,weproposeanewLagrangefunctionmethodandtheglobalconvergenceofthemethodcanalsobeproved.Thenumericalresultsshowthatthealgorithmhasgoodadaptabilityandstability.2.Thefirstequivalenttotheequalityconstraintsareconver
6、tedintotwoinequalityconstraints,thenusingthemethodinthelastchapter,turningthemintonewinequalityconstraints,Accordingtothecharacteristicsofthefunction,thetwoinequalityconstraintsfurtherequivalentlyconvertedintoaninequalityconstraint,sothecontainsequalitycon-strainedproblemintotheO
7、ptimizationproblemswhichonlyhaveinequalityconstraints.Finally,themethodofLagrangefunctionforgeneralconstrainedoptimizationproblemsisgiven.KeywordsLagrangemultipliermethod;KKT-system;Nonlinearconstraints;Exponentialfunction..........................................................
8、...........1§1.1........................
