Optimality Conditions Of Multi-Objective Programming Problems Involving A Class Of Generalized Convexity

This paper deals with the optimality conditions of nonsmooth multi-objective programming prob-lems involving generalized convexity. First, as generalized convex functions related to this article, bothB-arcwise connected functions and Type-I functions, are recalled the above two classes generalizedconvexity, some new functions are given, such as B-quasi-arcwise connected functions, B-pseudo-arcwiseconnected functions, B-arcwise connected Type-I functions and generalized B-arcwise connected Type-Ifunctions. Then, under the assumption of above generalized convexity, the optimality conditions and dualtheory for nonsmooth multi-objective programming problems are discussed. The main results obtained inthis dissertation can be summarized as follows:1. Based upon the B-arcwise connected functions, the concepts of B-quasi-arcwise connected func-tions and B-pseudo-arcwise connected functions are introduced, and their basic properties are investigated.2. Under the assumptions of B-arcwise connected convexity and generalized B-arcwise connectedconvexity, the Kuhn-Tucker and saddle points necessary and sufficient conditions are obtained for nons-mooth multi-objective programming problems.3. Combining with the definitions of B-arcwise connected functions and Type-I functions, the no-tions of B-arcwise connected Type-I functions and generalized B-arcwise connected Type-I functionsare introduced. The optimality conditions are established for nonsmooth multi-objective programmingproblems.4. Duality theory of nonsmooth multi-objective programming problems is considered. Three typeduality models including Mond-Weir type duality model, Wolfe type duality model and mixed type dualitymodel are constructed. And for above these dual models, weak duality theorems, the strong dualitytheorems and converse duality theorems are established.