文档介绍：.,36(4),541556(2015)—015—1929—9⑥ShanghaiUniversityandSpringer—VerlagBerlinHeidelberg2015AppliedMathematicsandMechanics(EnglishEdition),UniversityofL6dl,L6di90—238,—strainedoptimizationproblemareinvexwithrespecttothesamefunction卵(withtheexceptionofthoseequalityconstraintsforwhichtheassociatedLagrangemultipliersarenegative——thesefunctionsshouldbeassumedtobeincavewithrespectto卵).Thus,athresholdofthepenaltyparameterisgivensuchthat,forallpenaltyparametersexceedingthisthreshold,-,minimaxpenalizedoptimizationproblem,exactnessofpenalizationofexactminimaxpenaltyfunction,invexfunction,incavefunctionChineseLibraryClassification02422010MathematicsSubjectClassification49M30,90C26,90C301IntroductionTheextremumproblemconsideredinthispaperisageneralnonlinearconstrainedoptimiza—tionproblemwheref:X__+,gi:X-_÷(i∈),andhj:__÷R(J∈J),,2014/,2014十Correspondingauthor,E—mail:antczak~{一肌∈.Ⅲ.~≤=.,:={∈X:gi(x)≤0,i∈I,hj(x)=0,J∈}bethesetofallfeasiblesolutionsofProblem(P).Further,wedenotethesetofactiveconstraintsatthepoint∈Dby』()={∈I:(虿)=0)Now,wegivethegeneralizedSlaterconstraintqualifi