Mathematical Sciences: Algorithms for Convex Programming-Interior Point and Proximal Point Methods

数学科学：凸规划算法-内点法和近点法

• 批准号: 9306318
• 负责人: Osman Guler
• 金额: $ 6万
• 依托单位: University of Maryland Baltimore County
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-15 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9306318&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algorithms; Convex; Programming

This project will support research in the analysis and development of algorithms for large-scale convex programming problems. Two of the most versatile algorithms have been interior point methods and splitting methods based on the proximal point algorithm. Specific areas of research will include: (1) the interior point transformation, involving the analysis of the mapping in interior point methods that sends an interior feasible pair to its coordinatewise product; (2) infeasible interior point methods, including bridging the gap between the feasible and infeasible interior point methods; (3) convergence of the proximal point method, including the analysis of the global and local convergence behavior of the proximal point method and its modifications; and (4) interior point methods for nonlinear problems, involving the development of practical interior point methods, especially primal-dual methods, for special classes of nonlinear programs and monotone complementarity problems. Two of the most important modern algorithms for the numerical solution of large-scale convex programming problems have been interior point methods and proximal point methods. Both of these methods have had a major impact on modern numerical solution techniques for problems that were previously thought to be intractable because of their massive size.

该项目将支持分析研究， 大规模凸规划算法的发展 问题 两种最通用的算法是 内点法和基于内点法的分裂法 邻近点算法 具体研究领域将 包括：（1）内点变换，涉及 分析了内点方法中的映射， 坐标乘积的内部可行对;（2） 不可行的内点方法，包括弥合差距 可行内点法与不可行内点法之间的关系;（3） 近点法的收敛性，包括分析 的全局和局部收敛行为的近端 点法及其改进;（4）内点法 非线性问题的方法，包括发展 实用的内点方法，特别是原对偶方法， 对于一类特殊的非线性规划和单调 互补性问题。 两个最重要的现代算法， 大规模凸规划问题的数值解 有内点法和邻近点法。 这两种方法都对现代数值计算产生了重大影响。 解决技术的问题，以前认为， 由于其庞大的体积而难以处理。