The Mathematical Institute, University of Oxford, Eprints Archive

A Branch and Bound Algorithm for the Global Optimization of Hessian Lipschitz Continuous Functions

Fowkes, J. M. and Gould, N. I. M. and Farmer, C. L. (2012) A Branch and Bound Algorithm for the Global Optimization of Hessian Lipschitz Continuous Functions. Journal of Global Optimization . (Submitted)

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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.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1541
Deposited By:Peter Hudston
Deposited On:04 Jul 2012 09:05
Last Modified:04 Jul 2012 09:05

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