Stabilization of Mehrotra's primal–dual algorithm and its implementation

In this paper we apply a stabilization procedure proposed by Kovačević-Vujčić and Ašić to the Mehrotra's primal–dual interior-point algorithm for linear programming. Transformations of the dual problem corresponding to the stabilization procedure are considered. The stabilization procedure and...

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Bibliographic Details
Published inEuropean journal of operational research Vol. 165; no. 3; pp. 598 - 609
Main Authors STANIMIROVIC, Predrag S, STOJKOVIC, Nebojsa V, KOVACEVIC-VUJCIC, Vera V
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 16.09.2005
Elsevier
Elsevier Sequoia S.A
SeriesEuropean Journal of Operational Research
Subjects
Algorithms
Applied sciences
Degeneracy
Exact sciences and technology
Ill-conditioning
Linear programming
MATHEMATICA
Mathematical programming
Operational research and scientific management
Operational research. Management science
Operations research
Primal–dual interior-point methods
Stabilization
Studies
Ill-conditioning
Degeneracy
MATHEMATICA
Primal–dual interior-point methods
Stabilization
Primal dual method
Interior point method
Linear programming
Degeneration
Ill conditioned problem
Mathematical programming
Primal-dual interior-point methods
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Summary:In this paper we apply a stabilization procedure proposed by Kovačević-Vujčić and Ašić to the Mehrotra's primal–dual interior-point algorithm for linear programming. Transformations of the dual problem corresponding to the stabilization procedure are considered. The stabilization procedure and Mehrotra's algorithm are implemented in the package MATHEMATICA. A number of highly degenerate test examples are used to compare the modified Mehrotra's method with respect to the original one and the codes PCx, LIPSOL and MOSEK. We also provide numerical results on some examples from the Netlib test set.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2003.07.024