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Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Pearson, John W, Gondzio, Jacek (2017) Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization. Numerische Mathematik, 137 . pp. 959-999. ISSN 0029-599X. E-ISSN 0945-3245. (doi:10.1007/s00211-017-0892-8) (KAR id:53192)

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Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations.

Item Type: Article
DOI/Identification number: 10.1007/s00211-017-0892-8
Uncontrolled keywords: Interior point methods; PDE-constrained optimization; Krylov subspace methods; Preconditioning; Schur complement
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: 11 Dec 2015 16:22 UTC
Last Modified: 23 Mar 2021 16:09 UTC
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