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.
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Muu, L.D., Quy, N.V. A Global Optimization Method for Solving Convex Quadratic Bilevel Programming Problems. Journal of Global Optimization 26, 199–219 (2003). https://doi.org/10.1023/A:1023047900333
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DOI: https://doi.org/10.1023/A:1023047900333