Efficient Stochastic Descent Methods for PDE-Constrained Optimization with Uncertain Coefficients

In this thesis, we consider a convex, elliptic PDE-constrained optimal control problem that is subject to uncertainty. To solve this problem numerically we use three stochastic descent methods, namely the Stochastic Gradient method, the Stochastic Variance Reduced Gradient method and the Stochastic Adaptive Sampling method. We state theoretical convergence results for the three stochastic descent methods and present a setting in which we conduct numerical tests to compare the convergence behaviour and the CPU time. The numerical experiments show that a modification of the Stochastic Adaptive Sampling method in combination with the Barzilai-Borwein step size rule is the superior choice for the specific problem.publishe