Logarithmic barrier decomposition methods for semi-infinite programming

A computational study of some logarithmic barrier decomposition algorithms for semi-infinite programming is presented in this paper. The conceptual algorithm is a straightforward adaptation of the logarithmic barrier cutting plane algorithm which was presented recently by den Hartog et al. (Annals o...

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Bibliographic Details
Published in:International transactions in operational research Vol. 4; no. 4; pp. 285 - 303
Main Authors: Kaliski, J., Haglin, D., Roos, C., Terlaky, T.
Format: Journal Article
Language:English
Published: Elsevier Science 01.07.1997
Subjects:
Column generation
convex programming
cutting plane methods
interior point method
linear programming
logarithmic barrier function
quadratic programming
semi-infinite programming
Column generation
cutting plane methods
convex programming
interior point method
linear programming
semi-infinite programming
logarithmic barrier function
quadratic programming
ISSN:0969-6016, 1475-3995
Online Access:Get full text
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Summary:A computational study of some logarithmic barrier decomposition algorithms for semi-infinite programming is presented in this paper. The conceptual algorithm is a straightforward adaptation of the logarithmic barrier cutting plane algorithm which was presented recently by den Hartog et al. (Annals of Operations Research, 58, 69–98, 1995), to solve semi-infinite programming problems. Usually decomposition (cutting plane methods) use cutting planes to improve the localization of the given problem. In this paper we propose an extension which uses linear cuts to solve large scale, difficult real world problems. This algorithm uses both static and (doubly) dynamic enumeration of the parameter space and allows for multiple cuts to be simultaneously added for larger/difficult problems. The algorithm is implemented both on sequential and parallel computers. Implementation issues and parallelization strategies are discussed and encouraging computational results are presented.
ISSN:0969-6016
1475-3995
DOI:10.1016/S0969-6016(97)00018-X