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Optimal Adjustment Algorithm for <i>p</i> Coordinates and The Starting Point in Interior Point Methods

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Author(s): Carla T. L. S. Ghidini | Aurelio R. L. Oliveira | Jair Silva

Journal: American Journal of Operations Research
ISSN 2160-8830

Volume: 01;
Issue: 04;
Start page: 191;
Date: 2011;
Original page

Keywords: Von Neumann’s Algorithm | Mehrotra’s Heuristic | Interior Point Methods | Linear Programming

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.
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