多目标(半)无限DC规划问题最优条件和对偶理论研究

项目名称： 多目标(半)无限DC规划问题最优条件和对偶理论研究

项目编号： No.11201099

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： 屈绍建

作者单位： 哈尔滨工业大学

项目金额： 22万元

中文摘要： (半)无限规划是应用数学中非常活跃的一个研究分支，在工程设计、最优控制、信息技术以及经济均衡等方面具有广泛的应用。本项目拟针对一类特殊的(半)无限规划问题- - 多目标(半)无限DC规划问题展开研究，试图对该类优化问题的最优条件和对偶问题进行深入研究，具体内容包括：（1）将Farkas引理推广至由无限多DC函数构成的不等式系统上，在此基础上讨论多目标(半)无限DC规划问题的最优必要和充分条件，建立原问题的多目标(半)无限线性规划或凸规划近似问题，并分析两者最优解(弱有效解或有效解)之间的关系；（2）研究原问题的对偶问题，讨论其对偶理论，重点构建弱对偶定理、强对偶定理和逆对偶定理；（3）在上述工作基础上研究多目标(半)无限分式DC规划问题(带有无限多DC函数约束，目标函数中每个分式的分子和分母均为DC函数的多目标规划问题)的最优条件和对偶理论。

中文关键词： 多准则决策；DC规划；供应链；利率优化；近似点

英文摘要： (Semi-)Infinite programming is a very active research branch in applied mathemathics which has been widely applied in Engineering design, Optimal control, Information technology and Economic equilibrium. This project considers a special (semi-)infinite programming, that is, multiobjective (semi-)infinite DC programming in which every objective function and every constraint function can be decomposed into the difference of two convex functions. In this project, we will focus on the optimality conditions and duality theory for the multiobjective (semi-)infinite DC programming. Specifically, our contributions are threefolders: (1) Firstly, the Farkas lemma will be extended to the inequality systems including infinite DC functions. Then the optimal conditions will be established by the extended Farkas lemma which include both the optimally sufficient condition and the optimally necessary condition. The multiobjective (semi-)infinite linear or convex approximate programming to the original problem will also be proposed and the relationship of the optimal solutions to the primal problem and the approximate problem will also be analyzed. (2) Secondly, the dual problems will be given and the duality theories including the weak duality theory, strong duality theory and converse duality theorem will be presented. (3) Fin

英文关键词： multi-objective game；DC programs；supply chain；portfolio optimization； Proximal point