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Journal of Global Optimization

, Volume 26, Issue 2, pp 199–219 | Cite as

A Global Optimization Method for Solving Convex Quadratic Bilevel Programming Problems

  • Le Dung Muu
  • Nguyen Van Quy
Article

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.

Convex quadratic bilevel programming Merit function Saddle function Branch-and-bound algorithm Optimization over an equilibrium set 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Le Dung Muu
    • 1
  • Nguyen Van Quy
    • 2
  1. 1.Hanoi Institute of MathematicsBo HoVietnam
  2. 2.The Accounting and Finance University of HanoiDong Ngac, Tu Liem, HanoiVietnam

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