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A global optimization approach for the linear two-level program

Journal of Global Optimization volume 3, pages 1–23 (1993)Cite this article

Abstract

Linear two-level programming deals with optimization problems in which the constraint region is implicity determined by another optimization problem. Mathematical programs of this type arise in connection with policy problems to which the Stackelberg leader-follower game is applicable. In this paper, the linear two-level programming problem is restated as a global optimization problem and a new solution method based on this approach is developed. The most important feature of this new method is that it attempts to take full advantage of the structure in the constraints using some recent global optimization techniques. A small example is solved in order to illustrate the approach.

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Authors and Affiliations

  1. Institute of Mathematics, P.O. Box 631, BoHo, Hanoi, Vietnam

    Hoang Tuy

  2. Department of Mathematics, Linköping Institute of Technology, S-581 83, Linköping, Sweden

    Athanasios Migdalas & Peter Värbrand

Authors
  1. Hoang Tuy
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  2. Athanasios Migdalas
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  3. Peter Värbrand
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Additional information

The paper was completed while this author was visiting the Department of Mathematics of Linköping University.

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Tuy, H., Migdalas, A. & Värbrand, P. A global optimization approach for the linear two-level program. J Glob Optim 3, 1–23 (1993). https://doi.org/10.1007/BF01100237

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  • DOI: https://doi.org/10.1007/BF01100237

Key words

  • Linear two-level program
  • global optimization
  • Stackelberg game
  • reverse convex constraint programming
  • polyhedral annexation method