Second-Order Variational Analysis and Its Applications

二阶变分分析及其应用

• 批准号: 1512846
• 负责人: Boris Mordukhovich
• 金额: $ 35.24万
• 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: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2021-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1512846&HistoricalAwards=false
• 关键词: Second; Order; Variational; Analysis; Its

This project aims to develop efficient tools of mathematical analysis to investigate challenging problems arising in optimization, systems control, and other fields of applied mathematics unified under the name of variational analysis. This new form of analysis employs generalized differential calculus when the standard calculus methods are not available. The main motivation for developing these tools of analysis is to solve a number of practical problems of engineering, mechanics, and behavioral sciences. Results of this project arm researchers and practitioners with new machinery that make it possible to solve problems that provide valuable insight to practical issues.This project focuses on second-order variational analysis, which has been largely underinvestigated from both viewpoints of theoretical studies and practical applications. It carries out a systematic development of generalized differential tools of second-order analysis, with applications to the design and justification of numerical algorithms in nonsmooth optimization and related areas. Among other directions of research, the project applies second-order variational analysis to broad classes of finite-dimensional and infinite-dimensional variational systems, which go far beyond optimization and optimal control. Results will be beneficial to both applied mathematics and applied science communities.

该项目旨在开发有效的数学分析工具，以研究在最优化，系统控制和其他应用数学领域中出现的具有挑战性的问题，统一在变分分析的名称下。这种新形式的分析采用广义微分时，标准的微积分方法是不可用的。开发这些分析工具的主要动机是解决工程，力学和行为科学的一些实际问题。本项目的成果为研究人员和从业人员提供了新的解决问题的方法，为实际问题提供了有价值的见解。本项目以二阶变分分析为重点，从理论研究和实际应用的角度来看，这在很大程度上是研究不足的。 它进行了二阶分析的广义微分工具的系统开发，应用于非光滑优化及相关领域的数值算法的设计和论证。在其他研究方向中，该项目将二阶变分分析应用于广泛的有限维和无限维变分系统，这些系统远远超出了优化和最优控制。研究结果将有利于应用数学和应用科学界。