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Inner Approximation Method for a Reverse Convex Programming Problem

Author

Listed:
  • S. Yamada

    (Osaka University, Yamada-Oka)

  • T. Tanino

    (Osaka University, Yamada-Oka)

  • M. Inuiguchi

    (Osaka University, Yamada-Oka)

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.

Suggested Citation

  • S. Yamada & T. Tanino & M. Inuiguchi, 2000. "Inner Approximation Method for a Reverse Convex Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 355-389, November.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:2:d:10.1023_a:1026456730792
    DOI: 10.1023/A:1026456730792
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