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arXiv · 1806.05896

Interior Point Methods and Preconditioning for PDE-Constrained Optimization Problems Involving Sparsity Terms

John W. Pearson·Margherita Porcelli·Martin Stoll
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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 $\rm L^1$ 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.

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John W. Pearson, Margherita Porcelli, Martin Stoll. 2018-06-15. Interior Point Methods and Preconditioning for PDE-Constrained Optimization Problems Involving Sparsity Terms. https://arxiv.org/abs/1806.05896

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