Rescaled coordinate descent methods for linear programming

Dadush, Daniel, Végh, László A. ORCID: 0000-0003-1152-200X and Zambelli, Giacomo (2016) Rescaled coordinate descent methods for linear programming. In: Louveaux, Quentin and Skutella, Martin, (eds.) Integer Programming and Combinatorial Optimization. Lecture Notes in Computer Science. Springer Berlin / Heidelberg, Cham, Switzerland, pp. 26-37. ISBN 9783319334608

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Abstract

We propose two simple polynomial-time algorithms to find a positive solution to Ax=0Ax=0 . Both algorithms iterate between coordinate descent steps similar to von Neumann’s algorithm, and rescaling steps. In both cases, either the updating step leads to a substantial decrease in the norm, or we can infer that the condition measure is small and rescale in order to improve the geometry. We also show how the algorithms can be extended to find a solution of maximum support for the system Ax=0Ax=0 , x≥0x≥0 . This is an extended abstract. The missing proofs will be provided in the full version.

Item Type:	Book Section
Official URL:	http://www.springer.com/
Additional Information:	© 2016 Springer International Publishing Switzerland
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	05 Oct 2017 13:23
Last Modified:	13 Sep 2024 17:33
URI:	http://eprints.lse.ac.uk/id/eprint/84479

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