Methods of Variational Analysis in Optimization, Equilibria, and Control

优化、平衡和控制中的变分分析方法

基本信息

批准号：
0603846
负责人：
Boris Mordukhovich
金额：
$ 30万
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：
2006
资助国家：
美国
起止时间：
2006-08-01 至 2010-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0603846&HistoricalAwards=false
关键词：
Methods Variational Analysis Optimization Equilibria

项目摘要

The project deals with developing new methods of variational analysis and their applications to various problems in optimization, equilibria, and control. Since modern variational principles and techniques intrinsically relate to models and problems with nonsmooth data, a large part of the research concerns generalized differentiation theory of the first and second order for nonsmooth functions, sets, and set-valued mappings. The obtained methods and results of generalized differentiation will be applied to deriving new optimality and suboptimality conditions and sensitivity/stability characterizations in problems of mathematical programming, optimization and equilibrium problems with equilibrium constraints, optimal control of evolution inclusions and partial differential and functional differential equations, etc. The primary goal of this project is to develop applications of advanced techniques of optimization, variational analysis, and optimal control to practical problems arising in mechanics, economics, engineering, environmental science, etc. This is a very challenging issue, which requires the development of new mathematical methods dealing with non-classical objects and models as well as with complex control systems. The research will particularly concern models of welfare economics with public environment and also economies involving oligopolistic markets, feedback design of control systems functioning under uncertainty, and other applications to real-life problems.

该项目涉及开发新的变异分析方法及其在优化，均衡和控制方面的各种问题中的应用。由于现代变分原理和技术本质上与非平滑数据的模型和问题有关，因此研究的很大一部分涉及对非平滑函数，集合和设置值映射的第一和二阶的广义分化理论。获得的广义分化的方法和结果将应用于得出新的最佳和次要条件以及敏感性/稳定性特征，这些问题在数学编程，优化和平衡限制的问题中的问题中的均衡性限制，最佳控制，偏差和部分差异方程式的最佳靶向范围的最佳靶向范围的最佳靶向技术，以进行均衡的最佳控制等。机械，经济学，工程，环境科学等引起的实际问题。这是一个非常具有挑战性的问题，它需要开发与非经典对象和模型以及复杂控制系统有关的新数学方法。这项研究将特别涉及福利经济学与公共环境以及涉及寡头市场的经济，在不确定性下运作的控制系统的反馈设计以及对现实生活中问题的其他应用。