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

Pearson, John W and Gondzio, Jacek (2017) Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization. Numerische Mathematik, . ISSN 0029-599X. E-ISSN 0945-3245. (doi:https://doi.org/10.1007/s00211-017-0892-8) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided)

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Abstract

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
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: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: John Pearson
Date Deposited: 11 Dec 2015 16:22 UTC
Last Modified: 13 Sep 2017 10:35 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/53192 (The current URI for this page, for reference purposes)
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