An ellipsoidal branch and bound algorithm for global optimization

Details An ellipsoidal branch and bound algorithm for global optimization An ellipsoidal branch and bound algorithm for global optimization

2009-12-09

arxiv.org/abs/0912.1673v1

SIAM Journal on Optimization, vol. 20 (2009), p.740-758

Mathematics

Optimization and Control

19 pages

Scientific paper

A branch and bound algorithm is developed for global optimization. Branching in the algorithm is accomplished by subdividing the feasible set using ellipses. Lower bounds are obtained by replacing the concave part of the objective function by an affine underestimate. A ball approximation algorithm, obtained by generalizing of a scheme of Lin and Han, is used to solve the convex relaxation of the original problem. The ball approximation algorithm is compared to SEDUMI as well as to gradient projection algorithms using randomly generated test problems with a quadratic objective and ellipsoidal constraints.

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