Journal of Industrial and Management Optimization (JIMO)

Global optimization algorithm for solving bilevel programming problems with quadratic lower levels

Pages: 177 - 196, Volume 6, Issue 1, February 2010      doi:10.3934/jimo.2010.6.177

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Paul B. Hermanns - Department of Mathematics, University of Trier, 54286 Trier, Germany (email)
Nguyen Van Thoai - Department of Mathematics, University of Trier, 54286 Trier, Germany (email)

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.

Keywords:   Bilevel programming, nonconvex programming, branch and bound.
Mathematics Subject Classification:  Primary: 90C26; Secondary: 91A05.

Received: March 2009;      Revised: September 2009;      Available Online: November 2009.