Long-step primal-dual target-following algorithms for linear programming |
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Authors: | Benjamin Jansen Ccs Roos Tamás Terlaky Jean-Philippe Vial |
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Affiliation: | (1) Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands;(2) Department of Commercial and Industrial Economics, University of Geneva, 102 Bd Carl Vogt, 1211 Geneva 4, Switzerland |
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Abstract: | In this paper we propose a long-step target-following methodology for linear programming. This is a general framework, that enables us to analyze various long-step primal-dual algorithms in the literature in a short and uniform way. Among these are long-step central and weighted path-following methods and algorithms to compute a central point or a weighted center. Moreover, we use it to analyze a method with the property that starting from an initial noncentral point, generates iterates that simultaneously get closer to optimality and closer to centrality.This work is completed with the support of a research grant from SHELL.The first author is supported by the Dutch Organization for Scientific Research (NWO), grant 611-304-028.The fourth author is supported by the Swiss National Foundation for Scientific Research, grant 12-34002.92. |
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Keywords: | Interior-point method affine scaling method primal-dual method long-step method |
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