General-purpose preconditioning for regularized interior point methods

Jacek Gondzio; Spyridon Pougkakiotis; John W. Pearson

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arXiv · 2107.06822

General-purpose preconditioning for regularized interior point methods

Jacek Gondzio·Spyridon Pougkakiotis·John W. Pearson

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Abstract

In this paper we present general-purpose preconditioners for regularized augmented systems arising from optimization problems, and their corresponding normal equations. 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.

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Jacek Gondzio, Spyridon Pougkakiotis, John W. Pearson. 2021-07-14. General-purpose preconditioning for regularized interior point methods. https://arxiv.org/abs/2107.06822

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