PDE Constrained Optimization with Uncertain Data
Monday, March 14, 2016 - 3:00pm - 4:00pm
Many science and engineering problems lead to optimization problems governed by partial differential equations (PDEs), and in many of these problems some of the problem data are not known exactly. I focus on a class of such optimization problems where the uncertain data are modeled by random variables or random fields, and where decision variables (controls/designs) are deterministic and have to be computed before the uncertainty is observed. It is important that the uncertainty in problem data is adequately incorporated into the formulation of the optimization problem. The numerical solution of all such formulations require a sampling of random variables. Since the number of PDEs that have to be solved depends linearly on the number of samples, it is important key the overall number of samples low. I will review problem formulations, problem discretization/sampling approaches, and their implications for the numerical solution of PDE constrained optimization with uncertain data.