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

John Pearson, Margherita Porcelli, Martin Stoll

Research output: Contribution to journalArticlepeer-review

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 L1 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.
Original languageEnglish
Number of pages27
JournalNumerical Linear Algebra with Applications
Volume27
Issue number2
Early online date9 Dec 2019
DOIs
Publication statusPublished - 31 Mar 2020

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