An 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 po...
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| Vydané v: | IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028) Ročník 3; s. 521 - 526 vol.3 |
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| Hlavní autori: | , , , |
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| Jazyk: | English Japanese |
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IEEE
20.01.2003
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| ISBN: | 9780780357310, 0780357310 |
| ISSN: | 1062-922X |
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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 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 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 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 relaxed problems is an optimal solution of the original problem. |
| Author | Tatsumi, K. Yamada, S. Tanino, T. Inuiguchi, M. |
| Author_xml | – sequence: 1 givenname: S. surname: Yamada fullname: Yamada, S. organization: Dept. of Electron. & Inf. Syst., Osaka Univ., Japan – sequence: 2 givenname: T. surname: Tanino fullname: Tanino, T. – sequence: 3 givenname: M. surname: Inuiguchi fullname: Inuiguchi, M. – sequence: 4 givenname: K. surname: Tatsumi fullname: Tatsumi, K. |
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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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| SubjectTerms | Approximation algorithms Approximation methods Electronic mail Information systems Optimization methods |
| Title | An inner approximation method for a reverse convex programming problem |
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