A Global Optimization Method for Solving Convex Quadratic Bilevel Programming Problems

Authors:
Le Dung Muu;Nguyen Van Quy
Affiliations:
Hanoi Institute of Mathematics, P.O. Box 631, Bo Ho 10000, Hanoi, Vietnam/;The Accounting and Finance University of Hanoi, Dong Ngac, Tu Liem, Hanoi, Vietnam
Venue:
Journal of Global Optimization
Year:
2003

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Abstract

We use the merit function technique to formulate a linearly constrained bilevel convex quadratic problem as a convex program with an additional convex-d.c. constraint. To solve the latter problem we approximate it by convex programs with an additional convex-concave constraint using an adaptive simplicial subdivision. This approximation leads to a branch-and-bound algorithm for finding a global optimal solution to the bilevel convex quadratic problem. We illustrate our approach with an optimization problem over the equilibrium points of an n-person parametric noncooperative game.