Mathematical Sciences: Studies in Optimization, Nonsmooth Analysis, and Optimal Control

数学科学：优化、非光滑分析和最优控制研究

• 批准号: 9006224
• 负责人: Boris Mordukhovich
• 金额: $ 5.99万
• 依托单位: Wayne State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006224&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Optimization; Nonsmooth

This project will study general optimization and control problems with nonsmooth data and develop effective methods for the analysis and the solution of such problems based on their approximation by problems of a simpler nature. Using approximation methods, tools of nonconvex analysis connected with the concepts of generalized differentials, normals, and conjugate mappings will be developed. Various applications of these methods will be made to sensitivity analysis, controllability, stability, optimality conditions, and other aspects of optimization and control in numerous problems. Finite difference approximations for continuous-time optimal control systems with constraints will be analyzed. Application to modeling in engineering and related areas are expected.

该项目将研究非光滑数据的一般优化和控制问题，并开发有效的方法来分析和解决这些问题，这些问题基于更简单性质的问题的近似。使用近似方法，非凸分析工具与广义微分，法线和共轭映射的概念将被开发。这些方法将在许多问题的灵敏度分析、可控性、稳定性、最优性条件以及其他优化和控制方面得到不同的应用。本文将分析带约束的连续时间最优控制系统的有限差分逼近。应用于工程及相关领域的建模。