New Applications of Variational Analysis to Optimization and Control

Abstract

Abstract. We discuss new applications of advanced tools of variational analysis and generalized differentiation to a number of important problems in optimization theory, equilibria, optimal control, and feedback control design. The presented results are largely based on the recent work by the author and his collaborators. Among the main topics considered and briefly surveyed in this paper are new calculus rules for generalized differentiation of nonsmooth and set-valued mappings; necessary and sufficient conditions for new notions of linear subextremality and suboptimality in constrained problems; optimality conditions for mathematical problems with equilibrium constraints; necessary optimality conditions for optimistic bilevel programming with smooth and nonsmooth data; existence theorems and optimality conditions for various notions of Pareto-type optimality in problems of multiobjective optimization with vector-valued and set-valued cost mappings; Lipschitzian stability and metric regularity aspects for constrained and variational systems.