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

Handle URI:
http://hdl.handle.net/10754/597224
Title:
A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions
Authors:
Fowkes, Jaroslav M.; Gould, Nicholas I. M.; Farmer, Chris L.
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.
Citation:
Fowkes JM, Gould NIM, Farmer CL (2012) A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions. J Glob Optim 56: 1791–1815. Available: http://dx.doi.org/10.1007/s10898-012-9937-9.
Publisher:
Springer Nature
Journal:
Journal of Global Optimization
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
21-Jun-2012
DOI:
10.1007/s10898-012-9937-9
Type:
Article
ISSN:
0925-5001; 1573-2916
Sponsors:
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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorFowkes, Jaroslav M.en
dc.contributor.authorGould, Nicholas I. M.en
dc.contributor.authorFarmer, Chris L.en
dc.date.accessioned2016-02-25T12:28:20Zen
dc.date.available2016-02-25T12:28:20Zen
dc.date.issued2012-06-21en
dc.identifier.citationFowkes JM, Gould NIM, Farmer CL (2012) A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions. J Glob Optim 56: 1791–1815. Available: http://dx.doi.org/10.1007/s10898-012-9937-9.en
dc.identifier.issn0925-5001en
dc.identifier.issn1573-2916en
dc.identifier.doi10.1007/s10898-012-9937-9en
dc.identifier.urihttp://hdl.handle.net/10754/597224en
dc.description.abstractWe 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.en
dc.description.sponsorshipWe 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).en
dc.publisherSpringer Natureen
dc.subjectBranch and bounden
dc.subjectGlobal optimizationen
dc.subjectLipschitzian optimizationen
dc.subjectNonconvex programmingen
dc.titleA branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functionsen
dc.typeArticleen
dc.identifier.journalJournal of Global Optimizationen
dc.contributor.institutionUniversity of Edinburgh, Edinburgh, United Kingdomen
dc.contributor.institutionRutherford Appleton Laboratory, , United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.