不确定非凸规划的稳健全局优化方法的研究

项目名称： 不确定非凸规划的稳健全局优化方法的研究

项目编号： No.11426091

项目类型： 专项基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 吴丹

作者单位： 河南科技大学

项目金额： 3万元

中文摘要： 不确定性问题是人们在实际环境中时时处处会面对的。在非理想化的条件下，希望找到最优化的方案就必须考虑到不确定性所带来的各种风险。本项目以不确定非凸二次约束的二次规划问题为出发点，深入开展不确定非凸规划的稳健全局优化的研究和应用的讨论。基于稳健优化技术、全局优化方法与凸分析等知识，研究各类不确定集合（如矩形、椭球、或其它凸紧集等）下不确定非凸二次约束的二次规划问题的全局最优性条件及可解类。建立不确定非凸二次规划的对偶理论，给出稳健KKT条件，讨论保证稳健强对偶理论成立的约束规格。本项目的研究将拓展关于稳健非凸规划的研究，并为工程等实际问题的解决提供参考。

中文关键词： 不确定非凸规划；稳健（或分布式稳健）优化；稳健全局解；稳健对偶理论；全局优化算法

英文摘要： Uncertainty is ubiquitous in the real-world system. When decision makers attempt to find an optimal solution, the corresponding risk has been the subject of much speculation. This project aims to investigate non-convex quadratically constrained quadratic programming with data uncertainty, and the theme “researchs on robust global optimimization to non-convex programming problems under data uncertainty and its applications” has been deeply studied. Based on robust optimization technology, global optimization methods and convex analysis, non-convex quadratically constrained quadratic programming problems with the rectangular uncertainty set ,the simple ellipsoid uncertainty set and other convex compact uncertainty set are discussed respectively, and global optimality conditions of robust global optimal solutions and solvable subclasses are given. Duality in robust non-convex quadratic programming problems is established, the robust KKT condition is proposed, and constraint qualifications which guarantee for strong duality in robust optimization are discussed, respectively. The study of this project will expand researches on robust non-convex optimization, and provide references for the practical engineering problems.

英文关键词： Uncertain non-convex programming；(Distributionally) robust optimization；Robust global optimal solution；Duality in robust optimization；Global optimization algorithms