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January  2010, 6(1): 177-196. doi: 10.3934/jimo.2010.6.177

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

Paul B. Hermanns 1, and  Nguyen Van Thoai 1,

1. 

Department of Mathematics, University of Trier, 54286 Trier, Germany, Germany

Received  March 2009 Revised  September 2009 Published  November 2009

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: 91A0.
Citation: Paul B. Hermanns, Nguyen Van Thoai. Global optimization algorithm for solving bilevel programming problems with quadratic lower levels. Journal of Industrial and Management Optimization, 2010, 6 (1) : 177-196. doi: 10.3934/jimo.2010.6.177
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