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Variational Analysis in Problems of Optimization

最优化问题中的变分分析

基本信息

批准号：
0104055
负责人：
R. Tyrrell Rockafellar
金额：
$ 21.24万
依托单位：
University of Washington
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2001
资助国家：
美国
起止时间：
2001-08-01 至 2007-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0104055&HistoricalAwards=false
关键词：
Variational Analysis Problems Optimization

项目摘要

Pang, Jong-ShiFrom: Terry Rockafellar [rtr@math.washington.edu]Sent: Wednesday, June 13, 2001 3:59 PMTo: jpang@nsf.govSubject: proposal abstract Jong-Shih, here's the abstract for my proposal "Variational Analysis in Problems of Optimization". Terry ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This project will apply the latest advances in variational analysis to a range of optimization problems and issues. Sensitivity and metric regularity in parametric dependence will be studied. Second-order optimality conditions will be devised for new purposes and from nonstandard perspectives. Connections between cost-to-go functions and feedback for certain kinds of optimal control will be explored along with the specialization to a control framework of recently generalized Euler-Lagrange equations and Hamiltonian equations. New risk models and splitting algorithms will be developed in stochastic programming, where decisions must be made optimally in advance of full information. These efforts are needed because problems of optimization, which are of great importance in many applications from management to engineering, are not well covered by standard mathematics of the past and have required new ways of thinking. In such problems, centered on minimizing "cost" or maximizing "efficiency", for instance, there usually are very many side conditions that have to be satisfied, and moreover the number of decision variables to be coped with can be enormous---in the thousands or even millions. It is crucial to have a solid foundation for the development of numerical methods for finding solutions and understanding the effects that shifts in input data might have on those solutions. The work to be performed will further the progress in those directions.

来自：Terry Rockafellar [rtr@math.washington.edu]发送：2001年6月13日星期三下午3:59至：jpang@nsf.govSubject：提案摘要Jong-Shih，这是我的提案“优化问题中的变分分析”的摘要。Terry ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~这个项目将应用变分分析的最新进展来解决一系列优化问题。将研究参数依赖性的灵敏度和度量正则性。二阶最优性条件将被设计用于新的目的和从非标准的角度。对于某些类型的最优控制，成本函数和反馈之间的联系将随着最近推广的欧拉-拉格朗日方程和哈密顿方程的控制框架的专业化而被探索。新的风险模型和分割算法将在随机规划中发展，其中决策必须在充分信息之前做出最优。这些努力是必要的，因为优化问题在从管理到工程的许多应用中都非常重要，过去的标准数学没有很好地涵盖这些问题，需要新的思维方式。例如，在这类以最小化“成本”或最大化“效率”为中心的问题中，通常有很多必须满足的附带条件，而且需要处理的决策变量的数量可能是巨大的——数千甚至数百万。对于寻找解决方案和理解输入数据的变化可能对这些解决方案产生的影响的数值方法的发展来说，有一个坚实的基础是至关重要的。将要进行的工作将进一步推动这些方向的进展。