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Logarithmic Barrier Decomposition Methods for Semi‐infinite Programming
Author(s) -
Kaliski J.,
Haglin D.,
Roos C.,
Terlaky T.
Publication year - 1997
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/j.1475-3995.1997.tb00084.x
Subject(s) - logarithm , decomposition , cutting plane method , mathematical optimization , linear programming , computer science , dynamic programming , algorithm , criss cross algorithm , plane (geometry) , integer programming , mathematics , linear fractional programming , mathematical analysis , ecology , geometry , biology
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.