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

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