A Fast Solver for an $\mathcal{H}_1$ Regularized PDE-Constrained Optimization Problem (Communications in Computational Physics, 2018)
In this paper we consider PDE-constrained optimization problems which incorporatean $\mathcal{H}_1$ regularization control term. We focus on a time-dependent PDE, andconsider both distributed and boundary control. The problems we consider includebound constraints on the state, and we use a Moreau-Yosida penalty function to handlethis. We propose Krylov solvers and Schur complement preconditioning strategiesfor the different problems and illustrate their performance with numerical examples.