We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. Unlike other branch and bound algorithms, lower bounds are obtained via nonconvex underestimators of the function. For a numerical example, we apply the proposed branch and bound algorithm to radial basis function approximations. © 2012 Springer Science+Business Media, LLC.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: We would like to thank Coralia Cartis for helpful suggestions on an early draft of thispaper. We would also like to thank an anonymous referee for positive comments and revisions which havehelped improve the paper. This research was supported through an EPSRC Industrial CASE studentship inconjunction with Schlumberger. The work of Nick Gould was supported by the EPSRC grants EP/E053351/1,EP/F005369/1 and EP/I013067/1. This publication was also based on work supported in part by Award NoKUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (CLF).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.