A New Branch and Bound Method for Bilevel Linear Programs
A new branch and bound method is proposed for the Bilevel Linear Programming based on a transformation of the problem into a linear program with an additional reverse convex constraint. The method exploits the separated non-convexity and a monotonic property of the reverse convex constraint. Computational experiments are reported which show the efficiency of the approach for problems in which the matrix A2 is substantially smaller than the total number of variables.
KeywordsBilevel linear programming reverse convex constraint branch and bound simplicial subdivision
Unable to display preview. Download preview PDF.
- R. Horst and H. Tuy: 1993, ‘Global Optimization (Deterministic Approaches), Second Edition, Springer-Verlag, Berlin, New York.Google Scholar
- J.J. Judice and A.M. Faustino: 1988, ‘The solution of the linear bilevel programming problem by using the linear complementarity problem, Investigacao Oper., 8, 77–95.Google Scholar
- H. Thy: 1994, ‘Introduction to Global Optimization’, GERAD G-9404, Ecole Polytechnique de Montréal.Google Scholar
- H. Thy: 1995, ‘D.C. Optimization: Theory, Methods and Algorithms’ in eds. R. Horst and P.M. Pardalos Handbook on Global Optimization, Kluwer Academic Publishers, 149–216.Google Scholar
- H. Thy, A.Migdalas and P. Värbrand: 1992, ‘A Global Optimization Approach for the Linear Two-Level Program’, Journal of Global Optimization, 3, 1–23.Google Scholar