Mathematical Sciences: Infinite Dimensional Nonlinear Programming Problems-Optimal Control Theory of Partial Differential and Functional Differential Equations

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Work to be done on this project falls into two related classes. The first, infinite dimensional nonlinear programming problems, concerns the modeling of optimal control problems for partial differential equations, functional differential equations and other equations as infinite dimensional nonlinear programming problems. Goals include developing necessary conditions for the existence of minima and for the convergence of sequences of suboptimal elements. The second theme, optimal control theory of partial differential and functional differential equations concerns application of results from the first part to problems such as optimal deformation problems - especially in the presence of obstacles. The results are likely to include versions of Pontryagin's maximum principle, constancy and vanishing of the Hamiltonian and convergence estimates. Attention will also be given to boundary control questions, where results (compared to distributed parameter systems) are sparse. Application to specific equations will be made.