Inner approximation method for a reverse convex programming problem

Inner approximation method for a reverse convex programming problem

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Article ID: iaor2002422
Country: United States
Volume: 107
Issue: 2
Start Page Number: 355
End Page Number: 389
Publication Date: Nov 2000
Journal: Journal of Optimization Theory and Applications
Authors: , ,
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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