A Cutting Plane Algorithm for Linear Reverse Convex Programs
In this paper, global optimization of linear programs with an additional reverse convex constraint is considered. This type of problem arises in many applications such as engineering design, communications networks, and many management decision support systems with budget constraints and economies-o...
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| Published in: | Annals of operations research Vol. 105; no. 1-4; pp. 201 - 212 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Springer Nature B.V
01.07.2001
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| Subjects: | |
| ISSN: | 0254-5330, 1572-9338 |
| Online Access: | Get full text |
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| Summary: | In this paper, global optimization of linear programs with an additional reverse convex constraint is considered. This type of problem arises in many applications such as engineering design, communications networks, and many management decision support systems with budget constraints and economies-of-scale. The main difficulty with this type of problem is the presence of the complicated reverse convex constraint, which destroys the convexity and possibly the connectivity of the feasible region, putting the problem in a class of difficult and mathematically intractable problems. We present a cutting plane method within the scope of a branch-and-bound scheme that efficiently partitions the polytope associated with the linear constraints and systematically fathoms these portions through the use of the bounds. An upper bound and a lower bound for the optimal value is found and improved at each iteration. The algorithm terminates when all the generated subdivisions have been fathomed. [PUBLICATION ABSTRACT] |
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| Bibliography: | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| ISSN: | 0254-5330 1572-9338 |
| DOI: | 10.1023/A:1013361800945 |