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2010, Volume 6, Issue 1: 177-196. Doi: 10.3934/jimo.2010.6.177
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Global optimization algorithm for solving bilevel programming problems with quadratic lower levels

  • 1.

    Department of Mathematics, University of Trier, 54286 Trier

Received:  February 28, 2009
Revised:  August 31, 2009
Published:  December 2009
Abstract Related Papers Cited by
    Abstract
  • In this article, we propose a method for finding the global optimum of a class of nonlinear bilevel programming problems. The main idea of this method is to construct iteratively a sequence of points either ending at an optimal solution of the equivalent problem with a complementarity constraint, or converging to an optimal solution. The construction of such a sequence is performed by using a branch-and-bound scheme, together with some relaxation techniques, which are successfully applied in global optimization. Some illustrative examples and results on computational experiments are reported.
    Mathematics Subject Classification: Primary: 90C26; Secondary: 91A05.

    Citation:
    shu

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