Mathematical Sciences: Applications of Infinite Dimensional Nonsmooth Analysis to Optimization and Control

数学科学：无限维非光滑分析在优化和控制中的应用

• 批准号: 9404128
• 负责人: Boris Mordukhovich
• 金额: $ 11.89万
• 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: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404128&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Applications; Infinite; Dimensional

9404128 Mordukhovich/Ioffe This project is concerned with developing effective methods of infinite dimensional nonsmooth analysis and their applications to various problems in optimization and control theory. The main focus is on basic tools and calculus for generalized differentiation of nonsmooth mappings in Banach spaces, differential characterizations of openness, regularity, and related properties of infinite dimensional multifunctions, as well as on a broad spectrum of applications of nonsmooth analysis to optimal control of differential equations and inclusions, distributed parameter systems, and stability and sensitivity questions in constrained optimization and control theory. Nonsmooth analysis is concerned with the development of a calculus suitable for the analysis of functions which do not have the necessary smoothness properties that allow application of the standard calculus of variations. This investigation is largely motivated by important applications of nonsmooth calculus and variational analysis to problems arising in optimization and control of manufacturing systems. In particular, this work is related to minimax design of dynamical systems under uncertain conditions, stability of optimal solutions under parameter perturbations, and robust control of constrained distributed parameter systems. ***

9404128 Mordukhovich/Ioffe这个项目与开发无限尺寸非平滑分析的有效方法及其在优化和控制理论中的各种问题上的应用。主要的重点是用于基本工具和计算，用于在Banach空间中非平滑映射的一般差异，开放性，规律性和无限维度多功能函数的相关特性的差异特征，以及在非措施分析对差异方程式控制和含义的范围分析的广泛应用中的广泛应用，并分配了分配的参数和稳定性和稳定性，并有效地控制。 非平滑分析涉及用于用于分析功能分析的微积分的发展，而该功能没有必要的平滑度，可以应用标准的变化计算。这项调查在很大程度上是由非平滑微积分和变异分析在制造系统优化和控制中产生的问题的重要应用所激发的。特别是，这项工作与不确定条件下动态系统的最小值设计有关，参数扰动下的最佳解决方案的稳定性以及对约束分布式参数系统的强大控制。 ***