, Volume 35, Issue 2-4, pp 149-173
Date: 21 Jul 2011

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

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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.

Communicated by Rafael Bru.
The work of M. Benzi was supported in part by NSF grant DMS-0511336.
The work of E. Haber was supported in part by DOE under grant DEFG02-05ER25696, and by NSF under grants CCF-0427094, CCF-0728877, DMS-0724759 and DMS-0915121.