Interior Point Methods and Preconditioning for PDE-Constrained Optimization Problems Involving Sparsity Terms
Optimization and Control
2019-02-13 v2 Numerical Analysis
Abstract
PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting term within the objective function requires sophisticated optimization methods. We propose the use of an Interior Point scheme applied to a smoothed reformulation of the discretized problem, and illustrate that such a scheme exhibits robust performance with respect to parameter changes. To increase the potency of this method we introduce fast and efficient preconditioners which enable us to solve problems from a number of PDE applications in low iteration numbers and CPU times, even when the parameters involved are altered dramatically.
Cite
@article{arxiv.1806.05896,
title = {Interior Point Methods and Preconditioning for PDE-Constrained Optimization Problems Involving Sparsity Terms},
author = {John W. Pearson and Margherita Porcelli and Martin Stoll},
journal= {arXiv preprint arXiv:1806.05896},
year = {2019}
}