Optimization Problems in Banach Spaces with Non-smooth Structure

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The aim of this project is to develop and analyse algorithms for the numerical solution of some highly difficult optimization problems in Banach spaces. This includes mathematical programs with complementarity constraints, switching constraints, or problems involving a sparsity term either in the objective function or the constraints. By exploiting the special structure of these problems, the goal is to derive solution methods with strong global and local convergence properties under realistic, problem-tailored assumptions. All methods will be implemented and tested extensively on several relevant examples.