Mathematical Sciences: Studies in Optimization, Nonsmooth Analysis, and Optimal Control

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This project will study general optimization and control problems with nonsmooth data and develop effective methods for the analysis and the solution of such problems based on their approximation by problems of a simpler nature. Using approximation methods, tools of nonconvex analysis connected with the concepts of generalized differentials, normals, and conjugate mappings will be developed. Various applications of these methods will be made to sensitivity analysis, controllability, stability, optimality conditions, and other aspects of optimization and control in numerous problems. Finite difference approximations for continuous-time optimal control systems with constraints will be analyzed. Application to modeling in engineering and related areas are expected.