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

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Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXIV
Subtitle of host publicationDD 2017
PublisherSpringer
Pages503-510
Number of pages8
ISBN (Electronic)978-3-319-93873-8
ISBN (Print)978-3-319-93872-1
Publication statusPublished - 2018

Publication series

NameLecture Notes in Computational Science and Engineering
PublisherSpringer

Abstract

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.

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