Characterizations Of The Solution Sets For Several Nonlinear Optimization Problems

Convexity and the generalized convexity paly a very important role in mathematical economic, engineering, management science and optimization theory This paper is concerned with the properties and characterizations of solution sets for several classes of nonlinear optimizations under the invexity and generalized invexity.The outline of the thesis is as follows.In chapter1, we introduce the current situation of characterizations of solution sets for Nonlinear Optimization Problems.In chapter2, we present some preliminaries for the full article.In chapter3, we focus on thecharacterizations of solution sets for a class of nonlinear optimization problems by the Dini upper directional derivative. First of all, we present some properties of several generalized invexity,under the definition of Dini upper directional derivative. Second, some characterizations of the solution set for a class of nonlinear optimization problems are proved, in which the objective function is invex and the constraint functions are η-pseudolinear. Furthermore, we get further results for a new class of nonlinear optimization problems with the objective function and constraint functions are both η-pseudolinear.In chapter4, we propose some characterizations of the solution set for nonsmooth pseudoinvex optimization problem under the definition of Clarke subdifferential. Then some examples are given. In chapter5, we studied cone characterizations in two types of proper efficient points—Henig proper efficient points and Hurwicz proper efficient points in the objective space of general vector optimization problem.These were mainly presented with the help of contigent cones, normal cones and feasible directions cones of a set at a point.In chapter6, we give a summary of this paper and put forward some problems for further study.The innovation of this thesis mainly lies in the3-th,4-th,5-th chapters.