Optimality Conditions For Multiobjective Optimization Problems With Equilibrium Constrains

With equilibrium constraints, a multi-objective optimization problem is a special kind of optimization problem. This kind of problems, research on which involve in such mathematical branches as set-valued analysis, nonlinear analysis, non-smooth analysis, partial ordering theory, is one of the hot research topic in the vector optimization field and widely used in engineering design, financial investment, military and so on. Then people attach great importance to this problem and the research for them has important learning value. Because this kind of constraint, cause the problem is not easy to handle in both theoretical analysis and algorithm design.In studying equilibrium constraint optimization problem, the optimality conditions possess incomparable status, especially many valid algorithms need to be in the optimality conditions. This paper is devoted to research the necessary conditions for a class of multi-objective optimization programs with cone equilibrium constraints and with fixed-point equilibrium constrains.Firstly, we give brief introduction to the development and research significance of multi-objective optimization,and also summarize the developments associated with this thesis, thus bringing forth the main idea researched in this thesis. Secondly, we apply the related theory of variation analysis, transform this problem and present some equivalent forms for easy handling. Then under appropriate assumptions we further in-depth develop optimality conditions for multi-objective optimization problems with equilibrium constrains.In this paper we improve the theory of mathematical programming to a certain extent, and provide a theoretical basis of algorithms and some application of this kind problem in the future.