The Study Of Generalized Approximate Solution And Some Properties For Set-valued Optimization Problems

With the rapid development of set-valued optimization problem in economics, op-timal control, and so on. scholars pay more and more attentions on the approximate solution of set-valued optimization problems. This article mainly discuss a new defined approximate solution’s property, existence theorem and the connectivity of Henig approx-imate solution. Details are as follows:In the first chapter, we introduce the development process and preliminaries of set-valued optimization problem, including some basic concepts and some conclusions in Banach space and set-valued optimization problems.In the second chapter, we introduce the definition of generalized approximate solu-tion for set-valued maps, obtained some solution’s properties and it’s existence theorem. And compared with other approximate solution of set-valued optimization problem.In the third chapter, we prove the connectivity of Henig approximate solution by weakening the convexity, continuity and compactness of the objective function.