Matrix-free quadratic-penalty methods for PDE-constrained optimization

TitleMatrix-free quadratic-penalty methods for PDE-constrained optimization
Publication TypeConference
Year of Publication2015
AuthorsBas Peters, Felix J. Herrmann, Chen Greif
Conference NameSIAM Conference on Computational Science and Engineering
Keywordsleast-squares, low-rank, PDE-constrained optimization, quadratic-penalty, waveform inversion

The large scale of seismic waveform inversion makes matrix free implementations essential. We show how to exploit the quadratic penalty structure to construct matrix free reduced-space and full-space algorithms, which have some advantages over the commonly used Lagrangian based methods for PDE-constrained optimization. This includes the construction of effective and sparse Hessian approximations and reduced sensitivity to the initial guess. A computational bottleneck is the need to solve a large least squares problem with a PDE block. When direct solvers are not available, we propose a fast matrix free iterative approach with reasonable memory requirements. It takes advantage of the structure of the least squares problem with a combination of preconditioning, low rank decomposition and deflation.


(SIAM, Salt Lake City)

Citation Keypeters2015SIAMmfq