Optimal Control of Partial Differential Equations Involving Pointwise State Constraints: Regularization and Applications (English shop)

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Irwin Yousept’s dissertation investigates the optimal control of partial differential equations subject to pointwise state constraints. The research focuses on theoretical and numerical methods for solving complex optimization problems in which system states must satisfy prescribed bounds. Particular attention is given to Lavrentiev-type and Moreau-Yosida-type regularization techniques, which improve the mathematical and numerical treatment of state-constrained problems. The study examines first- and second-order optimality conditions and the convergence of locally optimal solutions. Sensitivity analyses with respect to regularization parameters are developed alongside extrapolation-based numerical algorithms. The semismooth Newton method is employed to efficiently solve the resulting optimization systems. Both distributed control and boundary control problems involving pointwise state constraints are investigated. Another central contribution concerns optimal control problems with nonlocal radiation interface conditions arising in semiconductor crystal growth. Applications include the sublimation growth of silicon carbide and aluminum nitride single crystals. The findings provide theoretical insights and numerical approaches for solving challenging PDE-constrained optimization problems.