Greedy Sampling Using Nonlinear Optimization

Abstract

We consider the reduced basis generation in the offline stage. As an alternative for standard Greedy-training methods based upon a-posteriori error estimates on a training subset of the parameter set, we consider a nonlinear optimization combined with a Greedy method. We define an optimization problem for selecting a new parameter value on a given reduced space. This new parameter is then used -in a Greedy fashion- to determine the corresponding snapshot and to update the reduced basis. We show the well-posedness of this nonlinear optimization problem and derive first- and second-order optimality conditions. Numerical comparisons with the standard Greedy-training method are shown.