Variational Analysis and its Applications

变分分析及其应用

• 批准号: 0304989
• 负责人: Boris Mordukhovich
• 金额: --
• 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: 2003
• 资助国家: 美国
• 起止时间: 2003-08-15 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0304989&HistoricalAwards=false
• 关键词: Variational; Analysis; its; Applications

This research project is devoted to the theory and applications of variational analysis, an active area in applied mathematics primarily concerned with optimization-related problems. It also applies variational techniques to the study of a broad range of problems that may not be of a variational nature. Since nonsmooth structures frequently and naturally appear in analysis and optimization, constructions and techniques of generalized differentiation lie at the heart of variational analysis and its applications. The project will mainly deal with developing the basic theory of variational analysis and generalized differentiation, with applications to important problems in optimization, control, stability, mechanics, and economics.Optimal decisions are required in various activities, including high-performance computing, manufacturing, environment and global change, etc. Variational analysis concerns mathematical methods of optimization that play a crucial role in many applications to complex systems in engineering, economics, and other areas of modern science and technology. This research project will focus on the development and application of efficient mathematical techniques for discovering optimal solutions in systems with complex structures. It particularly involves developing new methods of optimal control. This award is being jointly funded by the Division of Mathematical Sciences and the Directorate for Social, Behavioral, and Economic Sciences as part of the Mathematical Sciences Priority Area.

该研究项目致力于变异分析的理论和应用，这是一个主要与优化相关问题有关的应用数学领域的活跃领域。 它还将各种技术应用于对可能不是各种性质的广泛问题的研究。 由于非平滑结构经常自然出现在分析和优化中，因此广义分化的结构和技术位于变分分析及其应用的核心。 该项目将主要涉及发展变异分析和广义差异化的基本理论，并在优化，控制，稳定，力学，力学和经济学中适用于重要的问题。在各种活动中需要进行最佳的决策，包括高性能计算，制造，环境和全球变化等，等等的数学分析方法，即在许多技术方面的技术和许多技术在许多方面的技术和许多技术的应用程序。 该研究项目将着重于开发和应用有效的数学技术，以发现具有复杂结构的系统中的最佳解决方案。 它尤其涉及开发最佳控制的新方法。该奖项是由数学科学和社会，行为和经济科学局共同资助的，这是数学科学优先领域的一部分。