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

Jaroslav Fowkes(jaroslav.fowkes***at***ed.ac.uk)
Nicholas Gould(nick.gould***at***stfc.ac.uk)
Chris Farmer(Chris.Farmer***at***maths.ox.ac.uk)

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.

Keywords: Global Optimisation, Cubic Regularization, Radial Basis Function Approximation

Category 1: Global Optimization

Citation: Technical Report RAL-TR-2011-0200 Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, England

Download: [PDF]

Entry Submitted: 12/05/2011
Entry Accepted: 12/05/2011
Entry Last Modified: 12/05/2011

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