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On Block Triangular Preconditioners for the Interior Point Solution of PDE-Constrained Optimization Problems

Pearson, John W. and Gondzio, Jacek (2018) On Block Triangular Preconditioners for the Interior Point Solution of PDE-Constrained Optimization Problems. In: Domain Decomposition Methods in Science and Engineering XXIV. Lecture Notes in Computational Science and Engineering . Springer, Cham, Switzerland. ISBN 978-3-319-93872-1. E-ISBN 978-3-319-93873-8. (doi:10.1007/978-3-319-93873-8_48) (KAR id:61945)

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We consider the numerical solution of saddle point systems of equations resulting from the discretization of PDE-constrained optimization problems, with additional bound constraints on the state and control variables, using an interior point method. In particular, we derive a Bramble-Pasciak Conjugate Gradient method and a tailored block triangular preconditioner which may be applied within it. Crucial to the usage of the preconditioner are carefully chosen approximations of the (1,1)-block and Schur complement of the saddle point system. To apply the inverse of the Schur complement approximation, which is computationally the most expensive part of the preconditioner, one may then utilize methods such as multigrid or domain decomposition to handle individual sub-blocks of the matrix system.

Item Type: Book section
DOI/Identification number: 10.1007/978-3-319-93873-8_48
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: John Pearson
Date Deposited: 05 Jun 2017 10:21 UTC
Last Modified: 10 Dec 2022 05:56 UTC
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