A new proposal to improve the early iterations in the interior point method

Manolo Rodriguez Heredia () and Aurelio Ribeiro Leite Oliveira ()
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Manolo Rodriguez Heredia: Federal University of Southern and Southeastern Pará
Aurelio Ribeiro Leite Oliveira: University of Campinas

Annals of Operations Research, 2020, vol. 287, issue 1, No 8, 185-208

Abstract: Abstract We propose a modification that allows reducing the number of restarts in the computation of the Controlled Cholesky Factorization preconditioner. We use this preconditioner in the solution of linear systems arising from primal-dual interior point method. The Controlled Cholesky Factorization preconditioner depends on the fill-in parameter and the correction parameter that controls diagonal fault. We use geometric and algebraic tools to modify these parameters. In particular, we determine an equation whose exact solution avoids the diagonal fault. Numerical experiments with large-scale problems show that these modifications reduce the number of restarts. These experiments indicate that the new approach is robust and competitive.

Keywords: Interior point method; Conjugate gradient method; Preconditioner; Controlled Cholesky Factorization (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10479-019-03254-7

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