Faster Randomized Interior Point Methods for Tall/Wide Linear Programs

Agniva Chowdhury, Gregory Dexter, Palma London, Haim Avron, Petros Drineas

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such as combinatorics. It is also used in many machine learning applications, such as `1-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 both feasible and infeasible IPMs for the special case where the number of variables is much larger than the number of constraints. Using tools from Randomized Linear Algebra, we present a preconditioning technique that, when combined with the iterative solvers such as Conjugate Gradient or Chebyshev Iteration, provably guarantees that 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-world and synthetic data.

Original languageEnglish
Article number336
JournalJournal of Machine Learning Research
Volume23
StatePublished - 1 Sep 2022

Funding

FundersFunder number
Amazon Graduate Fellowship in Artificial Intelligence
Department of Statistics
National Science Foundation1814041, 1760353
U.S. Department of EnergySC0022085, DEAC05-00OR22725
Bloom's Syndrome Foundation2017698
Purdue University
UT-Battelle

    Keywords

    • Interior Point Methods
    • Linear Programming
    • Randomized Linear Algebra

    Fingerprint

    Dive into the research topics of 'Faster Randomized Interior Point Methods for Tall/Wide Linear Programs'. Together they form a unique fingerprint.

    Cite this