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A global optimization approach for the linear two-level program


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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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).

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Key words

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