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

作者：Benzi Michele^*; Haber Eldad; Taralli Lauren

来源：Advances in Computational Mathematics, 2011, 35(2-4): 149-173.

DOI：10.1007/s10444-011-9173-8

• Constrained optimization
• KKT conditions
• Saddle point problems
• Hyperbolic PDEs
• Krylov subspace methods
• Preconditioning
• Monge-Kantorovich problem
• Image registration

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.

• 出版日期2011-11