Optimality Conditions And Dulity For Multiobjective Programming

Multiobjective optimization problem is one of the main research field of optimization theory and applications. Study on which involves many disciplines, such as: convexity analysis, nonsmooth analysis, nonlinear functionals analysis, and so on. The theory and methods for the multiobjective optimization are widely used in the ares of modern economic planning, financial investment, engineering design, environmental protection,military, etc. In this thesis, we mainly study the theory of multiobjective optimization in two aspects: duality for multiobjective programming problems with cone constraints, the optimality conditions for approximate solutions of multiobjective programming problems.The main results, obtained in this dissertation, may be summarized as follows:1. In Chapter 1, firstly, we give brief introduction to the development and research significance of multiobjective optimization. And we also summarize the developments of the multiobjective optimization in two aspects associated with this thesis. Secondly, we recall some basic concepts and results. Finally, we outline the contents studied in this thesis.2. Chapter 2 is committed to study the duality for multiobjective optimization problems with cone constraints. First, we establish four dual models for multiobjective programming problem with cone constraints and discuss weak duality theorems, strong duality theorems and converse duality theorems by using Fritz John type necessary condition under generalized convexity assumptions. And then, we construct second-order and higher-order dual models and establish weak, strong and converse duality theorems.3. In chapter 3, we study the optimality conditions for approximate solutions for multiobjective optimization problems. Here, tangent cone,-normal cone, cones of feasible directions are used in the characterizations.