A locally adapted reduced basis method for solving risk-averse pde-constrained optimization problems
The numerical solution of risk-averse PDE-constrained optimization problems requires substantial computational effort resulting from the discretization of the underlying PDE in both the physical and stochastic dimensions. To practically solve problems with high-dimensional uncertainties, one must intelligently manage the individual discretization fidelities throughout the optimization iteration. In this work, we combine an inexact trust-region algorithm with the recently developed local reduced basis approximation to efficiently solve risk-averse optimization problems with PDE constraints. The main contribution of this work is a numerical framework for systematically constructing surrogate models for the trust-region subproblem and the objective function using local reduced basis approximations. We demonstrate the effectiveness of our approach through a numerical example.
