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J. P. M. Gon?alves, R. H. Storer and J. Gondzio, “A Family of Linear Programming Algorithms Based on an Algorithm by Von Neumann,” Optimization Methods and Software, Vol. 24, No. 3, 2009, pp. 461-478. doi:10.1080/10556780902797236

has been cited by the following article:

• TITLE: Optimal Adjustment Algorithm for p Coordinates and The Starting Point in Interior Point Methods

  AUTHORS: Carla T. L. S. Ghidini, Aurelio R. L. Oliveira, Jair Silva

  KEYWORDS: Von Neumann’s Algorithm, Mehrotra’s Heuristic, Interior Point Methods, Linear Programming

  JOURNAL NAME: American Journal of Operations Research, Vol.1 No.4, December 5, 2011

  ABSTRACT: Optimal adjustment algorithm for p coordinates is a generalization of the optimal pair adjustment algorithm for linear programming, which in turn is based on von Neumann’s algorithm. Its main advantages are simplicity and quick progress in the early iterations. In this work, to accelerate the convergence of the interior point method, few iterations of this generalized algorithm are applied to the Mehrotra’s heuristic, which determines the starting point for the interior point method in the PCx software. Computational experiments in a set of linear programming problems have shown that this approach reduces the total number of iterations and the running time for many of them, including large-scale ones.