Friday, November 25, 2016, 10:30
Room 02-016/18, Georges-Koehler-Allee 101, Freiburg 79110, Germany
We consider PDE-constrained optimization problems, where the partial differential equation has uncertain coefficients modelled by means of random variables or random fields. The goal of the optimization is to determine an optimum that is satisfactory in a broad parameter range, and as insensitive as possible to parameter uncertainties. First, an overview is given of different deterministic goal functions which achieve the above aim with a varying degree of robustness. Next, a multilevel Monte Carlo method is presented which allows the efficient calculation of the gradient and the Hessian arising in the optimization method. The convergence and computational complexity for different gradient and Hessian based methods is then illustrated for a model elliptic diffusion problem with lognormal diffusion coefficient. We demonstrate the efficiency of the algorithm, in particular for a large number of optimization variables and a large number of uncertainties.