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.

该项目将通过非平滑数据研究一般优化和控制问题，并根据其近似性，以简单性质的问题来开发有效的分析方法和解决这些问题的方法。 使用近似方法，将开发与广义差异，正态和共轭映射的概念相关的非convex分析工具。 这些方法的各种应用将用于敏感性分析，可控性，稳定性，最佳条件以及在许多问题中优化和控制的其他方面。 将分析具有约束的连续时间最佳控制系统的有限差近似值。 预计在工程和相关领域的建模应用。