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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Vydáno v:Journal of optimization theory and applications Ročník 107; číslo 2; s. 355 - 389
Hlavní autoři: Yamada, S., Tanino, T., Inuiguchi, M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY Springer 01.11.2000
Springer Nature B.V
Témata:
Algorithms
Applied sciences
Approximation
Engineering schools
Exact sciences and technology
Information systems
Mathematical functions
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Polytope
Penalty function
Global optimum
Duality
Convex programming
ISSN:0022-3239, 1573-2878
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Shrnutí: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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ISSN:0022-3239
1573-2878
DOI:10.1023/A:1026456730792