A preconditioning technique for a class of PDE-constrained optimization problems

Authors:
Michele Benzi;Eldad Haber;Lauren Taralli
Affiliations:
Department of Mathematics and Computer Science, Emory University, Atlanta, USA 30322;Department of Mathematics and Computer Science, Emory University, Atlanta, USA 30322 and Department of Mathematics, University of British Columbia, Vancouver, Canada V6T 1Z2;Quantitative Analytics Research Group, Standard & Poor's, New York, USA 10041
Venue:
Advances in Computational Mathematics
Year:
2011

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Abstract

We investigate the use of a preconditioning technique for solving linear systems of saddle point type arising from the application of an inexact Gauss---Newton scheme to PDE-constrained optimization problems with a hyperbolic constraint. The preconditioner is of block triangular form and involves diagonal perturbations of the (approximate) Hessian to insure nonsingularity and an approximate Schur complement. We establish some properties of the preconditioned saddle point systems and we present the results of numerical experiments illustrating the performance of the preconditioner on a model problem motivated by image registration.