Inner Approximation Method for a Reverse Convex Programming Problem
In this paper, we consider a reverse convex programming problem constrained by a convex set and a reverse convex set, which is defined by the complement of the interior of a compact convex set X. We propose an inner approximation method to solve the problem in the case where X is not necessarily a p...
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| Veröffentlicht in: | Journal of optimization theory and applications Jg. 107; H. 2; S. 355 - 389 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
Springer
01.11.2000
Springer Nature B.V |
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| ISSN: | 0022-3239, 1573-2878 |
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| Abstract | In this paper, we consider a reverse convex programming problem constrained by a convex set and a reverse convex set, which is defined by the complement of the interior of a compact convex set X. We propose an inner approximation method to solve the problem in the case where X is not necessarily a polytope. The algorithm utilizes an inner approximation of X by a sequence of polytopes to generate relaxed problems. It is shown that every accumulation point of the sequence of optimal solutions of the relaxed problems is an optimal solution of the original problem. |
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| AbstractList | In this paper, we consider a reverse convex programming problem constrained by a convex set and a reverse convex set, which is defined by the complement of the interior of a compact convex set X. We propose an inner approximation method to solve the problem in the case where X is not necessarily a polytope. The algorithm utilizes an inner approximation of X by a sequence of polytopes to generate relaxed problems. It is shown that every accumulation point of the sequence of optimal solutions of the relaxed problems is an optimal solution of the original problem. |
| Author | Inuiguchi, M. Yamada, S. Tanino, T. |
| Author_xml | – sequence: 1 givenname: S. surname: Yamada fullname: Yamada, S. – sequence: 2 givenname: T. surname: Tanino fullname: Tanino, T. – sequence: 3 givenname: M. surname: Inuiguchi fullname: Inuiguchi, M. |
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| Cites_doi | 10.1007/978-1-4615-2025-2 10.1515/9781400873173 10.1007/978-1-4757-2809-5 10.1007/978-3-662-03199-5 10.1137/1015073 10.1007/978-1-4615-4098-4 |
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| DOI | 10.1023/A:1026456730792 |
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| References | W. W. Hogan (228099_CR7) 1973; 15 R. Horst (228099_CR2) 1995 M. R. Hestenes (228099_CR6) 1975 R. Horst (228099_CR1) 1996 H. Konno (228099_CR3) 1997 H. Tuy (228099_CR4) 1998 R. T. Rockafellar (228099_CR5) 1970 M. S. Bazaraa (228099_CR8) 1993 |
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| Snippet | In this paper, we consider a reverse convex programming problem constrained by a convex set and a reverse convex set, which is defined by the complement of the... |
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| Title | Inner Approximation Method for a Reverse Convex Programming Problem |
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