Variational Analysis in Problems of Optimization

University Of Washington, Seattle WA

Investigators

Abstract

Pang, Jong-Shi From: Terry Rockafellar [rtr@math.washington.edu] Sent: Wednesday, June 13, 2001 3:59 PM To: jpang@nsf.gov Subject: 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.