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

Jaroslav Fowkes (), Nicholas Gould () and Chris Farmer ()

Journal of Global Optimization, 2013, vol. 56, issue 4, 1815 pages

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. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Global optimization; Lipschitzian optimization; Branch and bound; Nonconvex programming (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9937-9

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