Numerical Methods for Non-Smooth Optimization

非光滑优化的数值方法

• 批准号: 9731777
• 负责人: Michael Overton
• 金额: $ 25.5万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9731777&HistoricalAwards=false
• 关键词: Numerical; Methods; Non; Smooth; Optimization

Nonsmooth optimization problems involve objectives or constraints which are not differentiable everywhere. The term structured nonsmooth optimization means that the specific nonsmooth nature of the problem is known. One especially interesting class repeatedly arises in many applications: problems involving eigenvalues of matrices. The project primarily focuses on various aspects of eigenvalue optimization, including semidefinite programming, quasiconvex eigenvalue optimization, and non-Lipschitz eigenvalue optimization. The goal is fourfold: the development of fast, robust numerical algorithms; analysis of theoretical questions concerning optimality conditions and algorithm convergence; development of software which can be used by the general scientific community; and application to the solution of important interesting problems which arise in practice.

非光滑优化问题涉及并非处处可微的目标或约束。 术语“结构化非光滑优化”意味着问题的具体非光滑性质是已知的。 在许多应用中反复出现一类特别有趣的问题：涉及矩阵特征值的问题。 该项目主要关注特征值优化的各个方面，包括半定规划、拟凸特征值优化和非 Lipschitz 特征值优化。 目标有四个：开发快速、稳健的数值算法； 分析有关最优性条件和算法收敛性的理论问题；开发可供一般科学界使用的软件； 并应用于解决实践中出现的重要有趣问题。