Methods of Variational Analysis in Optimization, Equilibria, and Control

Wayne State University, Detroit MI

Investigators

Abstract

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.