Generalized Semi-(E,F)-Convex Functions And Their Applications In Multi Objective Semi-infinite Programming

In this paper,(E, F) invex set is defined based on the invex set and (E, F) convex set. And some classes of new generalized convex functions are given on the(E, F) invex set, those are semi (E, F) preinvex function, quasi semi (E, F) preinvex function, semi (E, F)ε preinvex function, and locally Lipschitz semi (E, F)ρ convex function, etc. Two classes of multiobjective semi-infinite programmingproblems are studied involving these generalized convex functions, such as someoptimality conditions and dual theory for local Lipschitz semi (E, F)ε generalizedconvex programming and some optimality conditions, saddle-points conditions Mond-Weir duality and Wolfe duality theorems for local Lipschitz semi (E, F)ρ generalizedconvex programming. The main contents of this paper include the following aspects:(1) Some classes of functions are defined based on preinvex function and semi (E, F) convex function, those are semi (E, F) preinvex function, quasi semi (E, F) preinvex function and semi (E, F)ε preinvex function. And some relevantproperties are given.(2) The optimality and Mond-Weir duality are studied for local Lipschitz semi (E, F)ε generalized convex multiobjective semi-infinite programming.(3) The definition of locally Lipschitz semi (E, F)ρ generalized convex functionis given. The optimality conditions, saddle-points conditions and the equivalencetheorem between saddle-points and optimal solutions for single objective programming.(4) Mond-Weir duality and Wolfe duality theory are studied for local Lipschitzsemi (E, F)ε generalized convex multiobjective semi-infinite programming, and someweak duality, strong duality and converse duality theorem are obtained. In summary, some classes of generalized convexities are presented in this paper thatextended the research of semi (E, F) convex function. In addition, the optimality,saddle-points conditions and duality theory are studied for multiobjective semi-infiniteprogramming involving these generalized semi (E, F) convexities, which enriched thecorresponding theory for multiobjective semi-infinite programming problems andgeneralized convexities.