joint work with Drew Philip Kouri
We propose a primal-dual algorithm for solving nonsmooth risk-averse optimization problems in Banach spaces motivated by PDE-constrained optimization under uncertainty. The overall algorithm is based on the well-known method of multipliers, whereas the subproblem solves are based on inexact Newton solvers for smooth PDE-constrained problems. The analysis exploits a number of recent results on the epigraphical regularization of risk measures. We prove convergence of the algorithm for solutions and stationary points and we conclude with several illustrative numerical examples
Development and quantitative validation of complex nonlinear dynamic models is a difficult task that requires the support by numerical methods for parameter estimation, and the optimal design of experiments. In this talk special emphasis is placed on issues of robustness, i.e. how to take into account uncertainties - such as outliers in the measurements for parameter estimation, and the dependence of optimal experiments on unknown values of model parameters. New numerical methods will be presented, and applications will be discussed that indicate a wide scope of applicability of the methods.
joint work with Stefan Vandewalle
This talk explores the use of multilevel quasi-Monte Carlo methods to generate estimations of gradients and Hessian-vector products for the optimization of PDEs with random coefficients. In ideal circumstances, the computational effort may scale linearly with the required accuracy, instead of quadratically, as is the case for Monte Carlo based methods. The performance is tested for a tracking type robust optimization problem constrained by an elliptic diffusion PDE with lognormal diffusion coefficient.