Accelerated sampling Kaczmarz Motzkin algorithm for the linear feasibility problem

Md Sarowar Morshed, Md Saiful Islam and Md. Noor-E-Alam ()
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Md Sarowar Morshed: Northeastern University
Md Saiful Islam: Northeastern University
Md. Noor-E-Alam: Northeastern University

Journal of Global Optimization, 2020, vol. 77, issue 2, No 8, 382 pages

Abstract: Abstract The Sampling Kaczmarz Motzkin (SKM) algorithm is a generalized method for solving large-scale linear systems of inequalities. Having its root in the relaxation method of Agmon, Schoenberg, and Motzkin and the randomized Kaczmarz method, SKM outperforms the state-of-the-art methods in solving large-scale Linear Feasibility (LF) problems. Motivated by SKM’s success, in this work, we propose an Accelerated Sampling Kaczmarz Motzkin (ASKM) algorithm which achieves better convergence compared to the standard SKM algorithm on ill-conditioned problems. We provide a thorough convergence analysis for the proposed accelerated algorithm and validate the results with various numerical experiments. We compare the performance and effectiveness of ASKM algorithm with SKM, Interior Point Method (IPM) and Active Set Method (ASM) on randomly generated instances as well as Netlib LPs. In most of the test instances, the proposed ASKM algorithm outperforms the other state-of-the-art methods.

Keywords: Kaczmarz method; Nesterov’s acceleration; Motzkin method; Sampling Kaczmarz Motzkin algorithm; 90C05; 65F10; 90C25; 15A39; 68W20 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-019-00850-6

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