DC programming techniques for solving a class of nonlinear bilevel programs

Authors:
Le Thi Hoai An;Pham Dinh Tao;Nam Nguyen Canh;Nguyen Thoai
Affiliations:
Laboratory of Theoretical and Applied Computer Science, UFR MIM, Metz University, Metz, France 57045;Laboratory of Modelling, Optimization and Operations Research, LMI, National Institute for Applied Sciences - Rouen, Mont Saint Aignan Cedex, France 76131;Laboratory of Modelling, Optimization and Operations Research, LMI, National Institute for Applied Sciences - Rouen, Mont Saint Aignan Cedex, France 76131;Department of Mathematics, University of Trier, Trier, Germany 54286
Venue:
Journal of Global Optimization
Year:
2009

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Abstract

We propose a method for finding a global solution of a class of nonlinear bilevel programs, in which the objective function in the first level is a DC function, and the second level consists of finding a Karush-Kuhn-Tucker point of a quadratic programming problem. This method is a combination of the local algorithm DCA in DC programming with a branch and bound scheme well known in discrete and global optimization. Computational results on a class of quadratic bilevel programs are reported.