Towards a practical parallelisation of the simplex method

Julian Hall (J.A.J.Halled.ac.uk)

Abstract: The simplex method is frequently the most efficient method of solving linear programming (LP) problems. This paper reviews previous attempts to parallelise the simplex method in relation to efficient serial simplex techniques and the nature of practical LP problems. For the major challenge of solving general large sparse LP problems, there has been no parallelisation of the simplex method that offers significantly improved performance over a good serial implementation. However, there has been some success in developing parallel solvers for LPs that are dense or have particular structural properties. As an outcome of the review, this paper identifies scope for future work towards the goal of developing parallel implementations of the simplex method that are of practical value.

Keywords: linear programming, simplex method, sparse, parallel computing

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: unpublished

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Entry Submitted: 02/17/2005
Entry Accepted: 02/17/2005
Entry Last Modified: 11/22/2007

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