A new preconditioning approach for an interior point-proximal method of multipliers for linear and convex quadratic programming

Luca Bergamaschi (Lead / Corresponding author), Jacek Gondzio, Angeles Martinez, John W. Pearson, Spyridon Pougkakiotis

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

In this article, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers, which in turn results in a primal-dual regularized interior point method. Application of this method gives rise to a sequence of increasingly ill-conditioned linear systems which cannot always be solved by factorization methods, due to memory and CPU time restrictions. We propose a novel preconditioning strategy which is based on a suitable sparsification of the normal equations matrix in the linear case, and also constitutes the foundation of a block-diagonal preconditioner to accelerate MINRES for linear systems arising from the solution of general quadratic programming problems. Numerical results for a range of test problems demonstrate the robustness of the proposed preconditioning strategy, together with its ability to solve linear systems of very large dimension.

Original languageEnglish
Article numbere2361
Number of pages19
JournalNumerical Linear Algebra with Applications
Volume28
Issue number4
Early online date7 Jan 2021
DOIs
Publication statusPublished - 1 Jul 2021

Keywords

  • BFGS update
  • interior point method
  • Krylov subspace methods
  • preconditioning
  • proximal method of multipliers

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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