向量优化问题的近似解的最优性条件

项目名称： 向量优化问题的近似解的最优性条件

项目编号： No.11201379

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 刘彩平

作者单位： 西南财经大学

项目金额： 22万元

中文摘要： 本项目主要研究向量优化问题的近似解的最优性条件。应用凸分析、非线性分析、非光滑分析和变分分析等理论和方法，研究向量优化问题近似解的线性标量化和非线性标量化性质，建立向量优化问题近似解与标量优化问题近似解之间的等价关系；应用广义次微分或者广义方向导数，研究向量优化问题近似解的Kuhn-Tucker型最优性条件和对偶定理；研究向量变分不等式的近似解，建立向量优化问题的近似解与向量变分不等式近似解之间的等价关系；引入新的近似真有效解概念，建立新引入的近似真有效解的最优性条件。本项目的研究旨在丰富和发展向量优化问题的近似解理论，为求解向量优化问题的近似解提供理论基础。

中文关键词： 向量优化；近似解；最优性条件；对偶性；广义凸性

英文摘要： The aims of this project is to study optimality conditions of approximate solutions in vector optimization. Applying the theory and methods of convex analysis, nonlinear analysis, nonsmooth analysis and variational analysis etc, linear scalarization and nonlinear scalarization of approximate solutions for vector optimization are studied, and the equivalence relationships between approximate solutions of vector optimization and the scalar optimization are established; the Kuhn-Tucker optimality conditions and duality theorem of approximate solutions in vector optimization are studied by generalized subdifferential or the generalized directional derivative; the approximate solutions of vector variational inequalities are studied, the equivalence relationships between approximate solutions of the vector optimization problems and the variational inequalities are established; the new concept of approximate proper efficient solutions are introduced, and its optimality conditions are given. The purpose of this project is to develop and increase the theory of approximate solutions in vector optimization, to provide a theoretical basis for solving vector optimization problems.

英文关键词： Vector Optimization；Approximate Solutions；Optimality Conditions；Duality；Generalized convexity