A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions

Jaroslav M. Fowkes, Nicholas I. M. Gould, Chris L. Farmer

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

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.
Original languageEnglish (US)
Pages (from-to)1791-1815
Number of pages25
JournalJournal of Global Optimization
Volume56
Issue number4
DOIs
StatePublished - Jun 21 2012
Externally publishedYes

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