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

Article

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.

Keywords

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

Mathematics Subject Classifications (2010)

65F08 65F22 49M05 49M15 90C30 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  3. 3.Quantitative Analytics Research GroupStandard & Poor’sNew YorkUSA

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