A family of linear programming algorithms based on an algorithm by von Neumann

Authors:
Joao P. M. Goncalves;Robert H. Storer;Jacek Gondzio
Affiliations:
Mathematical Sciences Department, IBM T. J. Watson Research Center, Yorktown Heights, NY, USA;Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA;School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, UK
Venue:
Optimization Methods & Software
Year:
2009

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Abstract

In this article, we present a family of algorithms for linear programming based on an algorithm proposed by von Neumann. The von Neumann algorithm is very attractive due to its simplicity, but is not practical for solving most linear programs to optimality due to its slow convergence. Our algorithms were developed with the objective of improving the practical convergence of the von Neumann algorithm while maintaining its attractive features. We present results from computational experiments on a set of linear programming problems that show significant improvements over the von Neumann algorithm.