Mathematical Sciences: Applications of Infinite Dimensional Nonsmooth Analysis to Optimization and Control

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9404128 Mordukhovich/Ioffe This project is concerned with developing effective methods of infinite dimensional nonsmooth analysis and their applications to various problems in optimization and control theory. The main focus is on basic tools and calculus for generalized differentiation of nonsmooth mappings in Banach spaces, differential characterizations of openness, regularity, and related properties of infinite dimensional multifunctions, as well as on a broad spectrum of applications of nonsmooth analysis to optimal control of differential equations and inclusions, distributed parameter systems, and stability and sensitivity questions in constrained optimization and control theory. Nonsmooth analysis is concerned with the development of a calculus suitable for the analysis of functions which do not have the necessary smoothness properties that allow application of the standard calculus of variations. This investigation is largely motivated by important applications of nonsmooth calculus and variational analysis to problems arising in optimization and control of manufacturing systems. In particular, this work is related to minimax design of dynamical systems under uncertain conditions, stability of optimal solutions under parameter perturbations, and robust control of constrained distributed parameter systems. ***