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

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  • Jaroslav Fowkes
  • Nicholas Gould
  • Chris Farmer

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

Suggested Citation

  • Jaroslav Fowkes & Nicholas Gould & Chris Farmer, 2013. "A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions," Journal of Global Optimization, Springer, vol. 56(4), pages 1791-1815, August.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:4:p:1791-1815
    DOI: 10.1007/s10898-012-9937-9
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    1. NESTEROV, Yurii & POLYAK, B.T., 2006. "Cubic regularization of Newton method and its global performance," LIDAM Reprints CORE 1927, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. R. Cavoretto & A. Rossi & M. S. Mukhametzhanov & Ya. D. Sergeyev, 2021. "On the search of the shape parameter in radial basis functions using univariate global optimization methods," Journal of Global Optimization, Springer, vol. 79(2), pages 305-327, February.
    2. Ruben van de Geer & Arnoud V. den Boer, 2022. "Price Optimization Under the Finite-Mixture Logit Model," Management Science, INFORMS, vol. 68(10), pages 7480-7496, October.
    3. Abdullah Al-Dujaili & S. Suresh & N. Sundararajan, 2016. "MSO: a framework for bound-constrained black-box global optimization algorithms," Journal of Global Optimization, Springer, vol. 66(4), pages 811-845, December.

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