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.
Bibliographical noteFunding Information:
* Corresponding author. E-mail: firstname.lastname@example.org. ! 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.
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- Column generation
- Logarithmic barrier
- Semi-infinite linear programming