Mathematical Sciences: Optimal Control Problems and Nonsmooth Analysis

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The principal investigator will conduct research on problems of optimal control, both in continuous and discrete time. Optimality conditions recently obtained for the control of differential inclusions will be applied to Bolza problems, and results are to be derived for Hamilton-Jacobi theory and feedback rules. In addition, a new theory of generalized second- derivatives will be applied to sensitivity analysis and parametric methods of optimization. Optimal control problems are useful as mathematical models in many areas of engineering and operations management. By better understanding their structure and properties, the gained insight will lead to improved numerical optimization algorithms.