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

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 preconditioner performance on a model problem motivated by image registration.