Predictor-Corrector Smoothing Methods for Linear Programs with a More Flexible Update of the Smoothing Parameter

Authors:
Stephan Engelke;Christian Kanzow
Affiliations:
Department of Mathematics, Center for Optimization and Approximation, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany. engelke@math.uni-hamburg.de;Institute of Applied Mathematics and Statistics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany. kanzow@mathematik.uni-wuerzburg.de
Venue:
Computational Optimization and Applications
Year:
2002

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Abstract

We consider a smoothing-type method for the solution of linear programs. Its main idea is to reformulate the corresponding central path conditions as a nonlinear system of equations, to which a variant of Newton's method is applied. The method is shown to be globally and locally quadratically convergent under suitable assumptions. In contrast to a number of recently proposed smoothing-type methods, the current work allows a more flexible updating of the smoothing parameter. Furthermore, compared with previous smoothing-type methods, the current implementation of the new method gives significantly better numerical results on the netlib test suite.