The Approximate Karush-kuhn-tucker Point Of Optimization Problems

The theory and method of optimization problems in mathematics is a very important research field, it is widely used for economic planning, government decision-making, produc-tion management, transportation, military defense and scientific management for many of the field. One of the core of the optimization problem is the existence of solutions for the problems, the approximate KKT conditions are the necessary conditions for the optimization problem have solution. This paper makes a study of the exception of optimization problems with approximate KKT point. This paper is organized as follows:In chapter1, we introduce the AKKT point of optimization problems and the present study situation conditions, and introduced the exceptional family of elements history. More-over, we recall some basic conceptions and notations which are used in this dissertation.In chapter2, we introduce the AKKT point of optimization problems. In the reflexive Banach space X, we research AKKT point of the convex optimization problem, meanwhile, we defined the AKKT point of optimization problem and continuous variational inequality problem Ⅵ(K, F) in Rn. Finally, we use scalar optimization method to research vector optimization problem and vector inequality problem, we defined the AKKT point of them.In chapter3, we introduce the SAKKT point and the weak efficient solutions of optimiza-tion problem, discuss the relationship between the SAKKT point of optimization problem and the weak efficient solutions of optimization problem.In chapter4, we use the conclusions of chapter2, according to the concept of exceptional family of elements, mainly discuss the relationship between AKKT point of optimization problem and exceptional family of elements. And prove that when the optimization problem have AKKT point, it must have no exceptional family. Finally, for the standard convex programming problem, we use different method, also prove the same conclusions.