The Theory Research For Multiobjective Semi-infinite Programming Involving Generalized Unified （C，α，p，d）-Convexity

In this paper, firstly, the definition of several classes of generalized convex functionsare presented by means the concepts of Clarke generalized subdifferential, that is,generalized unified (C，α，p，d) convex functions, generalized unified (C，α，p，d) qu-asi-convex functions, generalized unified (C，α，p，d)(strictly)pseudo-convex functionsand generalized unified (C，α，p，d) strong pseudo-convex functions. Secondly, theoptimality, Wolfe duality, Mond-Weir duality and saddle point criterion formultiobjective semi-infinite programming are studied involving these generalizedconvexities. At last,(C，α，p，d) V convex functions are proposed, and the mixedduality for multiobjective programming is researched involving these generalizedconvexities. The main achievements contained in this dissertation are as follow:1. Several classes of generalized convexities are defined based on(C,,, d) convexfunctions, and the optimality conditions are obtained involving these generalizedconvexities.2. The Mond-Weir duality and Wolfe duality for multiobjective semi-infiniteprogramming are studied involving these generalized unified (C，α，p，d) convexities.And the weak duality theorems, strong duality theorems and direct duality theorems areobtained.3. The definition of (C，α，p，d)-V-convex function is given. A mixed typicalduality for multiobjective variational problems is first formulated involving thesegeneralized convexities, which includes Wolfe type and Mond-Weir type duals as itsspecial cases. And we got some weak duality theorems and strong duality theorems.4. Saddle point optimality for multiobjective semi-infinite programming are researched involving generalized unified (C，α，p，d)convex functions.In all, some classes of generalized convexities are presented in this paper, and thenthe optimality, duality, and saddle point criterions for multiobjective semi-infiniteprogramming are studied involving these generalized convexities. these results enrichedthe corresponding theory for multiobjective semi-infinite programming problems andgeneralized convexities.