Complexity analysis of logarithmic barrier decomposition methods for semi-infinite linear programming

Zhi Quan Luo, C. Roos, T. Terlaky

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

In this paper, we analyze a logarithmic barrier decomposition method for solving a semi-infinite linear programming problem. This method is in some respects similar to the column generation methods using analytic centers. Although the method was found to be very efficient in the recent computational studies, its theoretical convergence or complexity is still unknown except in the (finite) case of linear programming. In this paper we present a complexity analysis of this method in the general semi-infinite case. Our complexity estimate is given in terms of the problem dimension, the radius of the largest Euclidean ball contained in the feasible set, and the desired accuracy of the approximate solution.

Original languageEnglish (US)
Pages (from-to)379-394
Number of pages16
JournalApplied Numerical Mathematics
Volume29
Issue number3
DOIs
StatePublished - Mar 1999

Bibliographical note

Funding Information:
* Corresponding author. E-mail: luozq@mcmaster.ca. ! The research of the first author is supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. OPG0090391, and by the Department of Operations Research of Delft University of Technology where he performed this research while on an academic visit.

Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

Keywords

  • Column generation
  • Decomposition
  • Logarithmic barrier
  • Semi-infinite linear programming

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