General-purpose preconditioning for regularized interior point methods

Jacek Gondzio; Spyridon Pougkakiotis; John W. Pearson

doi:10.1007/s10589-022-00424-5

General-purpose preconditioning for regularized interior point methods

Jacek Gondzio, Spyridon Pougkakiotis (Lead / Corresponding author), John W. Pearson

Mathematics

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1 Citation (Scopus)

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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
Number of pages	31
Journal	Computational Optimization and Applications
Volume	83
Issue number	3
Early online date	14 Nov 2022
DOIs	https://doi.org/10.1007/s10589-022-00424-5
Publication status	Published - Dec 2022

Keywords

Convex optimization
Interior point methods
Krylov subspace methods
Preconditioning
Regularization
Saddle point systems

ASJC Scopus subject areas

Control and Optimization
Computational Mathematics
Applied Mathematics

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10.1007/s10589-022-00424-5Licence: CC BY

Final published versionFinal published version, 2.35 MBLicence: CC BY

Cite this

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AU - Gondzio, Jacek

AU - Pougkakiotis, Spyridon

AU - Pearson, John W.

PY - 2022/12

Y1 - 2022/12

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.

KW - Convex optimization

KW - Interior point methods

KW - Krylov subspace methods

KW - Preconditioning

KW - Regularization

KW - Saddle point systems

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JF - Computational Optimization and Applications

IS - 3

ER -

General-purpose preconditioning for regularized interior point methods

Abstract

Keywords

ASJC Scopus subject areas

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Preconditioners for Regularized IPMs

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