A Fast Solver for an $\mathcal{H}_1$ Regularized PDE-Constrained Optimization Problem

doi:10.4208/cicp.190914.080415a

A Fast Solver for an $\mathcal{H}_1$ Regularized PDE-Constrained Optimization Problem

$A Fast Solver for an $\mathcal{H}_1$ Regularized PDE-Constrained Optimization Problem$

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Year: 2016

Communications in Computational Physics, Vol. 19 (2016), Iss. 1 : pp. 143–167

Abstract

In this paper we consider PDE-constrained optimization problems which incorporate an $\mathcal{H}_1$ regularization control term. We focus on a time-dependent PDE, and consider both distributed and boundary control. The problems we consider include bound constraints on the state, and we use a Moreau-Yosida penalty function to handle this. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.

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Journal Article Details

Publisher Name: Global Science Press

Language: English

DOI: https://doi.org/10.4208/cicp.190914.080415a

Communications in Computational Physics, Vol. 19 (2016), Iss. 1 : pp. 143–167

Published online: 2016-01

AMS Subject Headings: Global Science Press

Pages: 25

Keywords:

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