MAXIMUM ENTROPY METHODS FOR CONSTRAINED OPTIMIZATION AND MINIMAX PROBLEMS

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A NECESSARY AND SUFFICIENT CONDITION FOR A POINT TO BE A GLOBAL MAXIMIZER OF A CONSTRAINED OPTIMIZATION

It is difficult to judge whether a given point is a global maximizer of an unconstrained optimization problem. This paper deals with this problem by considering global information via integral and gives a necessary and sufficient condition judging whether a given point is a global maximizer of an unconstrained optimization problem. An algorithm is offered under such a condition and finally two test problems are verified via the offered algorithm.     

A MATHEMATICAL PROGRAMMING MODEL FOR THE COEXISTENCE OF COMPETITIONS AND COOPERATIONS PROBLEMS

We study in this paper a mathematical programming model for the coexistence of competitions and cooperations problems. We introduce a new solution concept, s-optimal solution for the problem, which always exists under compact and continuous conditions. It is shown that an s-optimal solution can be obtained by solving a nonlinear programming problem. Some examples are given to explain how to compute an s-optimal solution.     

POSITIVE SOLUTIONS FOR DIRICHLET PROBLEMS OF SINGULAR SEMILINEAR ELLIPTIC EQUATIONS

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OPTIMALITY CONDITIONS FOR NONCONVEX BILEVEL PROGRAMMING PROBLEMS

Recomendation.ThisworkisrecomendedbyamemberiftheEditorialBoard,ProfWANGShouyang.1.IntroductionThebilevelprogrammingproblemcanbestatedasfollows:whereS(x),foreachx,isthesolutionsetofthefollowingparametricprogrammingproblem:whereF,f:Re ~-R,g'Re ~-R"andG:Re ~…     

A NEW METHOD FOR FINDING MAJOR EFFICIENT SOLUTIONS AND MAJOR OPTIMAL SOLUTIONS OF DISCRETE MULTIOBJECTIVE PROGRAMMING

1.IntroductionThetermefficiencyisalsoknownasadmissibility,ornoninferiority.Itdepictsthemultiobjectiveprogrammingfromtheangleofsatisfaction.Majorefficiencyisbasedonthelawofmajority,whichhasbeenilitensivilyinvestigatedinpapers[1--3].Theprimaryconceptsaremajorefficientsolutionandmajoroptimalsolution.Considerthefollowingmultiobjectiveprogramming:whereXCRisthefeasibleregion,f:X~ac,f(x)=(fi(x),f200,'',fm(x)),andfi:X~Risareal-valuedfunction,acandacareEuclideanspaces.oIntroducetwoconesetsHandH…