Inner Approximation Method for a Reverse Convex Programming Problem

S. Yamada, T. Tanino and M. Inuiguchi
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S. Yamada: Osaka University, Yamada-Oka
T. Tanino: Osaka University, Yamada-Oka
M. Inuiguchi: Osaka University, Yamada-Oka

Journal of Optimization Theory and Applications, 2000, vol. 107, issue 2, No 9, 355-389

Abstract: 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.

Keywords: global optimization; reverse convex programming problem; dual problem; inner approximation method; penalty function method (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1026456730792

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