Journal
JOURNAL OF GLOBAL OPTIMIZATION
Volume 26, Issue 2, Pages 199-219Publisher
KLUWER ACADEMIC PUBL
DOI: 10.1023/A:1023047900333
Keywords
convex quadratic bilevel programming; merit function; saddle function; branch-and-bound algorithm; optimization over an equilibrium set
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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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