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General-purpose preconditioning for regularized interior point methods

Jacek Gondzio (), Spyridon Pougkakiotis () and John W. Pearson ()
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Jacek Gondzio: University of Edinburgh
Spyridon Pougkakiotis: Yale University
John W. Pearson: University of Edinburgh

Computational Optimization and Applications, 2022, vol. 83, issue 3, No 2, 727-757

Abstract: 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.

Keywords: Preconditioning; Krylov subspace methods; Interior point methods; Regularization; Saddle point systems; Convex optimization (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-022-00424-5

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