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Journal of Optimization Theory and Applications

, Volume 107, Issue 2, pp 355–389 | Cite as

Inner Approximation Method for a Reverse Convex Programming Problem

  • S. Yamada
  • T. Tanino
  • M. Inuiguchi
Article

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.

global optimization reverse convex programming problem dual problem inner approximation method penalty function method 

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References

  1. 1.
    Horst, R., and Tuy, H., Global Optimization: Deterministic Approaches, 3rd Edition, Springer Verlag, Berlin, Germany, 1996.Google Scholar
  2. 2.
    Horst, R., and Pardalos, P. M., Handbook of Global Optimization, Kluwer Academic Publishers, Dordrecht, Netherlands, 1995.Google Scholar
  3. 3.
    Konno, H., Thach, P. T., and Tuy, H., Optimization on Low-Rank Nonconvex Structures, Kluwer Academic Publishers, Dordrecht, Netherlands, 1997.Google Scholar
  4. 4.
    Tuy, H., Convex Analysis and Global Optimization, Kluwer Academic Publishers, Dordrecht, Netherlands, 1998.Google Scholar
  5. 5.
    Rockafellar, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.Google Scholar
  6. 6.
    Hestenes, M. R., Optimization Theory: The Finite-Dimensional Case, John Wiley, New York, NY, 1975.Google Scholar
  7. 7.
    Hogan, W. W., Point-to-Set Maps in Mathematical Programming, SIAM Review, Vol. 15, pp. 591–603, 1973.Google Scholar
  8. 8.
    Bazaraa, M. S., Sherali, H. D., and Shetty, C. M., Nonlinear Programming: Theory and Algorithms, 2nd Edition, John Wiley, New York, NY, 1993.Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • S. Yamada
    • 1
  • T. Tanino
    • 2
  • M. Inuiguchi
    • 3
  1. 1.Department of Electronics and Information Systems, Graduate School of EngineeringOsaka University, Yamada-OkaOsakaJapan
  2. 2.Department of Electronics and Information Systems, Graduate School of EngineeringOsaka University, Yamada-OkaOsakaJapan
  3. 3.Department of Electronics and Information Systems, Graduate School of EngineeringOsaka University, Yamada-OkaOsakaJapan

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