Research on Variational Analysis and Applications

变分分析及其应用研究

• 批准号: 9704751
• 负责人: Boris Mordukhovich
• 金额: $ 10.2万
• 依托单位: Wayne State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704751&HistoricalAwards=false
• 关键词: Research; Variational; Analysis; Applications

9704751 Mordukhovich This project will support research on variational analysis and its applications. Particular areas of research will include: nonconvex generalized differentiation of nonsmooth and set-valued mappings between Banach spaces; new characterizations and applications of robust Lipschitzian stability in infinite dimensions; sensitivity analysis of solution maps for parametric generalized equations and variational inequalities; discrete approximations and optimal control of constrained functional differential inclusions; and robust control design of uncertain evolutionary systems with hard control and state constraints. Variational analysis has been recognized as an active area of modern applied mathematics that, on one hand, deals with solving large-scale optimization and related problems and, on the other hand, applies optimization and perturbation ideas to the analysis of a broad spectrum of mathematical models arising in real-life applications. In particular, one of the proposal goals is to apply variational methods to feedback control design of evolutionary systems motivated by environmental applications.

9704751 Mordukhovich该项目将支持有关分析及其应用的研究。特定的研究领域将包括：非凸的普遍分化的非平滑度和固定值映射之间的跨度映射；强大的Lipschitzian稳定性在无限维度中的新特征和应用；解决参数概括方程和变异不平等的溶液图的敏感性分析； 离散的近似和最佳控制功能差异包含；以及具有硬控制和状态限制的不确定进化系统的强大控制设计。 变异分析被认为是现代应用数学的活跃领域，一方面，它涉及解决大规模优化和相关问题，另一方面，将优化和扰动思想应用于对现实生活应用中引起的广泛数学模型的分析。特别是，提案目标之一是将各种方法应用于由环境应用激励的进化系统的反馈控制设计。