非凸半无限规划理论若干新问题研究

项目名称： 非凸半无限规划理论若干新问题研究

项目编号： No.11471059

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 龙宪军

作者单位： 重庆工商大学

项目金额： 60万元

中文摘要： 本项目主要围绕非凸半无限规划理论若干新问题展开研究。利用非凸分离定理获得非凸半无限规划问题解/近似解存在的必要和充分条件以及对偶理论，刻画其解集/近似解集的连通性和适定性；借助新的约束规格，获得半无限多目标规划问题解的最优性条件和对偶理论；利用变分分析相关知识，获得非凸半无限多目标规划问题解集映射的半连续性、Lipschitz连续性、平静性以及Aubin性质等；借助共轭函数的上图性质引入较弱的约束规格，并用其来获得DC（半）无限（多目标）规划问题的稳定强对偶、全对偶、零对偶、Fenchel-Lagrange对偶以及Toland-Fenchel-Lagrange对偶。上述问题的研究不仅可以丰富和发展半无限规划问题的理论、方法和技巧，而且还可以为逼近问题、经济均衡、最优控制以及信息技术等领域中的大量实际问题提供新的理论工具和方法，对学科和社会经济发展具有重要意义.

中文关键词： 非凸半无限规划；半无限多目标规划；最优性条件；对偶性；稳定性

英文摘要： This project studies some new problems for the theory of nonconvex semi-infinite programming. By nonconvex separate theorems, the necessary and sufficiency optimality conditions and duality for solutions /approximate solutions of nonconvex semi-infinite programmings are obtained. Connectedness and well-posedness of solutions set/approximate solutions set and stability of the solution mapping for nonconvex semi-infinite programmings are derived. By new constraint qualification, the optimality conditions and duality for semi-infinite multiobjective programmings are obtained. By variational analysis, the semi-continuity, Lipschitz continuity, calmness and Aubin propery of the solution mapping for nonconvex semi-infinite multiobjective programmings are derived. By using the properties of the epigraph of the conjugated functions, some weaker constraint qualifications are introduced which completely characterize the stable duality, total duality, zero duality, Fenchel-Lagrange duality and Toland-Fenchel- Lagrange duality for DC (or semi-infinite)infinite (or multiobjective) programming. The study of above problems can not only enrich and develop the theory, methods and techniques of semi-infinite programmings, but also provide some new theoretical tools and methods for approximation problems, economic equilibrium, optimization control theory and information technology. And it is very important significance to the subject and the development of soci-economic.

英文关键词： nonconvex semi-infinite programming;semi-infinite multiobjective programming;optimization condition;duality;stability