The Generalized Semi-Infinite Programming With Inequality Constrains

Semi-infinite programming has wide applications in many fields such as economic equilibrium, optimal control, information technology and computer network. It is an important research part in the field of applied mathemat-ics.Recently,with the development of high technology and the profound research on the social economy, a large number of mathematical models of generalized semi-infinite programming emerge in these fields, in which the optimal value functions are generalized by non-compact sets or set-valued mappings instead of constant compact sets.Obviously,the generalized Nash equilibrium is the special ease of that. In generalized Nash equilibrium,the strategy set of each player is not a constant set which is independent of the strategy that others choose.Therefore,it is very significant to study the generalized semi-infinite programming.This dissertation is devoted to the study of sup-type function on non-compact set and the first-order optimality conditions for generalized semi-infinite programming with inequality constraints. This paper is composed of three chapters.Chapter 1 is the introduction of this paper, which introduce the development of semi-infinite programming and the main results in this paper.In chapter 2, the differential property of the sup-type function with a non-compact set is studied. The expression of its lower-Hadamard directional derivative is obtained. And the expression of its subdifferential is developed in the case that the effective domain of the sup-type function is a non-empty convex set.In chapter 3,we study the generalized semi-infinite programming with in-equality constraints. Using the lower-Hadamard directional derivative and subd-ifferential obtained in chapter 2, we get the first-order optimality condition and the equivalent form for the model (GSICP).