General-purpose preconditioning for regularized interior point methods

Jacek Gondzio; Spyros Pougkakiotis; John W Pearson

doi:10.1007/s10589-022-00424-5

General-purpose preconditioning for regularized interior point methods

Jacek Gondzio, Spyros Pougkakiotis^*, John W Pearson

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from optimization problems. We discuss positive definite preconditioners, suitable for CG and MINRES. We consider “sparsifications" which avoid situations in which eigenvalues of the preconditioned matrix may become complex. Special attention is given to systems arising from the application of regularized interior point methods to linear or nonlinear convex programming problems.

Original language	English
Pages (from-to)	727-757
Journal	Computational optimization and applications
Volume	83
Early online date	14 Nov 2022
DOIs	https://doi.org/10.1007/s10589-022-00424-5
Publication status	Published - 31 Dec 2022

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10.1007/s10589-022-00424-5

Modern linear algebra for PDE-constrained optimisation models for huge-scale data analysis
Pearson, J. (Principal Investigator)
EPSRC
1/10/19 → 31/03/23
Project: Research

Cite this

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title = "General-purpose preconditioning for regularized interior point methods",

abstract = "In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from optimization problems. We discuss positive definite preconditioners, suitable for CG and MINRES. We consider “sparsifications{"} which avoid situations in which eigenvalues of the preconditioned matrix may become complex. Special attention is given to systems arising from the application of regularized interior point methods to linear or nonlinear convex programming problems.",

author = "Jacek Gondzio and Spyros Pougkakiotis and Pearson, {John W}",

note = "Funding Information: The authors are grateful to the two anonymous referees for their valuable comments. JG and SP were supported by the Google project “Fast (1 + x)-order Methods for Linear Programming{"}. JWP gratefully acknowledges support from the Engineering and Physical Sciences Research Council (UK) grant EP/S027785/1. We wish to remark that this study does not have any conflict of interest to disclose. Publisher Copyright: {\textcopyright} 2022, The Author(s).",

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doi = "10.1007/s10589-022-00424-5",

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T1 - General-purpose preconditioning for regularized interior point methods

AU - Gondzio, Jacek

AU - Pougkakiotis, Spyros

AU - Pearson, John W

N1 - Funding Information: The authors are grateful to the two anonymous referees for their valuable comments. JG and SP were supported by the Google project “Fast (1 + x)-order Methods for Linear Programming". JWP gratefully acknowledges support from the Engineering and Physical Sciences Research Council (UK) grant EP/S027785/1. We wish to remark that this study does not have any conflict of interest to disclose. Publisher Copyright: © 2022, The Author(s).

PY - 2022/12/31

Y1 - 2022/12/31

N2 - In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from optimization problems. We discuss positive definite preconditioners, suitable for CG and MINRES. We consider “sparsifications" which avoid situations in which eigenvalues of the preconditioned matrix may become complex. Special attention is given to systems arising from the application of regularized interior point methods to linear or nonlinear convex programming problems.

AB - In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from optimization problems. We discuss positive definite preconditioners, suitable for CG and MINRES. We consider “sparsifications" which avoid situations in which eigenvalues of the preconditioned matrix may become complex. Special attention is given to systems arising from the application of regularized interior point methods to linear or nonlinear convex programming problems.

U2 - 10.1007/s10589-022-00424-5

DO - 10.1007/s10589-022-00424-5

M3 - Article

SN - 0926-6003

VL - 83

SP - 727

EP - 757

JO - Computational optimization and applications

JF - Computational optimization and applications

ER -

General-purpose preconditioning for regularized interior point methods

Abstract

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Modern linear algebra for PDE-constrained optimisation models for huge-scale data analysis

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