Faster randomized infeasible interior point methods for tall/wide linear programs

Agniva Chowdhury, Palma London, Haim Avron, Petros Drineas

Research output: Contribution to journalConference articlepeer-review

Abstract

Linear programming (LP) is used in many machine learning applications, such as l1-regularized SVMs, basis pursuit, nonnegative matrix factorization, etc. Interior Point Methods (IPMs) are one of the most popular methods to solve LPs both in theory and in practice. Their underlying complexity is dominated by the cost of solving a system of linear equations at each iteration. In this paper, we consider infeasible IPMs for the special case where the number of variables is much larger than the number of constraints (i.e., wide), or vice-versa (i.e., tall) by taking the dual. Using tools from Randomized Linear Algebra, we present a preconditioning technique that, when combined with the Conjugate Gradient iterative solver, provably guarantees that infeasible IPM algorithms (suitably modified to account for the error incurred by the approximate solver), converge to a feasible, approximately optimal solution, without increasing their iteration complexity. Our empirical evaluations verify our theoretical results on both real and synthetic data.

Original languageEnglish
JournalAdvances in Neural Information Processing Systems
Volume2020-December
StatePublished - 2020
Event34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online
Duration: 6 Dec 202012 Dec 2020

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