多目标规划问题的近似解及其相关问题研究

多目标规划问题有很强的实际应用背景，其研究工作不仅能推动运筹学理论自身的发展、解决许多实际问题，而且对包括纯粹数学在内的诸多相关领域的研究工作有积极的推动作用。本项目重点研究多目标规划问题近似解中的几个问题：(1)多目标规划问题近似解的研究：提出多目标规划问题新的近似解概念，研究其存在性、收敛性和近似最优性条件等。(2)研究多目标规划问题各种解（特别是真有效解和近似解）的标量化特征：利用非线性标量化函数、在非凸分离定理的基础上研究各种解的非线性标量化特征；通过引进新的广义凸函数类来研究各种解的线性标量化特征；研究非线性标量化函数的微分性质，并在标量化结果的基础上研究各种解的Lagrange乘子法则和对偶理论。(3)研究向量变分不等式问题的近似解:引进新的近似解概念，研究与相应的多目标规划问题近似解之间的关系和近似最优性条件等。

Multiobjective optimization problems has strong practical background. The research of multiobjective optimization problems can not only promote the own development of Operation Research Theory, and solve many practical problems, but also promote many other areas of relevant research works. This project focuses on the study of approximate solutions for multiobjective optimization problems,the main researches are as follows: (1)We will study approximate solutions of multiobjective optimization problems.That is, we will introduce several new approximate solutions for mutiobjective optimization problems and study their existence and convergence theory. (2) We will study the scalarizations of several kinds of solutions for multiobjective optimization problems,especially properly efficient solutions and approximate solutions. That is, we will study nonlinear scalarizations for several kinds of solutions, under the nonconvex seperation theorems. We will study the differential properties of nonlinear scalar functions, and lagrange multipliers and duality theorems will be derived. (3) We will study approximate solutions of vector variational inequality problems. That is, several new kinds of approximate solutions for vector variational inequality problems will be introduced, and we will study the relations with the approximate solutions of multiobjective optimization problems and their optimality conditions.