The Study Of The Duality Theorem For Multiobjective Programming

Multiobjective programming problems is a great important class of optimizationproblem, because most of the optimization problems in our real life are multiobjective.And in multiobjective programming research, the dual theory research is one of theimportant research directions. It plays an important role in searching the solution ofmultiobjective optimization and optimality condition. Moreover, convexprogramming problem is an important and basic class of optimization problem,however, many programs are nonconvex. So as to meet the demand of solvingpractical problems, many generalizations to convexity have been made, among whichthe G invexity is an important form. Therefore, it is significant to study the dualitytheorem of multiobjective programming problem under G invexity. This paper isconcerned with the duality theorem of two classes of multiobjective programmingproblems. One of them is nondifferentiable multiobjective programming, the other ismultiobjective semi-infinite programming.The outline of the thesis is as follows.In chapter1, we introduce the research significance of multiobjective dualitytheorem and current situation of related problems.In chapter2, we present some preliminaries and models for the full article.In chapter3, we focus on the duality theory for nondifferentiable G invexmultiobjective programs. First of all, we introduce G Karush-Kuhn-Tuckernecessary optimality condition for such problem. Second, the Mond-Weir dual models(NMWD1) and (NMWD2) are proposed, we study its dual results.(NMWD2)improve (NMWD1) through changing the constrained conditions of (NMWD1), sothat better results can be obtained. Third, we define G lagrange function and Wolfedual model, weak duality,strong duality and converse duality are proved. Especially,we establish the converse duality and one of the weak duality under invex assumptionwhich imposed on G lagrange function. At last, related to (NMWD1) and(NMWD2), we present mixed dual models (NMD1) and (NMD2). Also we obtain thecorresponding dual results these two models and its primal problem. In chapter4, we give the dual results for differentiable multiobjective semi-infinite programming under G invex assumption. Also we proposed three dualmodels, Mond-Weir,Wolfe and mixed duality, the corresponding dual theorems areproved.In chapter5, we give a summary of this paper and put forward some problemsfor further study.The innovation of this thesis lies in the3-th,4-th chapter.