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. © 2011 Springer Science+Business Media, LLC.

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

Benzi, Michele;
2011

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. © 2011 Springer Science+Business Media, LLC.
2011
Constrained optimization; Hyperbolic PDEs; Image registration; KKT conditions; Krylov subspace methods; Monge-Kantorovich problem; Preconditioning; Saddle point problems; Computational Mathematics; Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/75301
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