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

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Original languageEnglish
Number of pages27
JournalNumerical Linear Algebra with Applications
Publication statusAccepted/In press - 5 Nov 2019

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.

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