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Global Optimization and the Geometric Complementarity Problem

  • Reiner Horst
  • N. V. Thoai

Abstract

We survey briefly recent studies on the relationship between global optimization and the problem of finding a point in the difference of two convex sets (Geometric Complementarity Problem GCP). This relationship is of interest because, for large problem classes, transcending stationarity is equivalent to a special GCP. Moreover, the complementarity viewpoint often leads to dimension reduction techniques which can substantially reduce the computational effort of solving certain special-structured global optimization problems.

Keywords

Global Optimization Linear Complementarity Problem Global Optimization Problem Convex Minimization Problem Dimension Reduction Technique 
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References

  1. HORST, R. and TUY, H. (1991), ‘The Geometric Complementarity Problem and Transcending Stationarity in Global Optimization’, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Volume 4, Applied Geometry and Discrete Mathematic, The Victor Klee Festschrift, (Gritzmann, P. and Sturmfels, H. (eds.)), 341–345.Google Scholar
  2. HORST, R. and TUY, H. (1993), Global Optimization, 2nd edition, Springer, Berlin.Google Scholar
  3. MURTY, K.E. (1988), Linear Complementarity, Linear and Nonlinear Programming Heldermann, Berlin.Google Scholar
  4. ROCKAFELLAR, R.T. (1970), Convex Analysis, Princeton University Press, Princeton, N.Y.Google Scholar
  5. TUY, H. (1992), ‘The Complementary Convex Structure in Global Optimization’, Journal of Global Optimization 2, 21–40.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1993

Authors and Affiliations

  • Reiner Horst
  • N. V. Thoai
    • 1
  1. 1.FB IV — MathematikUniversity of TrierTrierGermany

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