A penalty method for PDE-constrained optimization

TitleA penalty method for {PDE}-constrained optimization
Publication TypeTech Report
Year of Publication2013
AuthorsTristan van Leeuwen, Felix J. Herrmann
NumberTR-EOAS-2013-6
PublisherUBC
KeywordsOptimization, private, waveform inversion
Abstract

We present a method for solving PDE constrained optimization problems based on a penalty formulation. This method aims to combine advantages of both full-space and reduced methods by exploiting a large search-space (consisting of both control and state variables) while allowing for an efficient implementation that avoids storing and updating the state-variables. This leads to a method that has roughly the same per-iteration complexity as conventional reduced approaches while dening an objective that is less non-linear in the control variable by implicitly relaxing the constraint. We apply the method to a seismic inverse problem where it leads to a particularly ecient implementation when compared to a conventional reduced approach as it avoids the use of adjoint state-variables. Numerical examples illustrate the approach and suggest that the proposed formulation can indeed mitigate some of the well-known problems with local minima in the seismic inverse problem.

URLhttps://www.slim.eos.ubc.ca/Publications/Private/TechReport/2013/vanLeeuwen2013Penalty2/vanLeeuwen2013Penalty2.pdf
Citation KeyvanLeeuwen2013Penalty2