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)
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.
|Subjects:||D - G > General|
|Research Groups:||Oxford Centre for Collaborative Applied Mathematics|
|Deposited By:||Peter Hudston|
|Deposited On:||04 Jul 2012 09:05|
|Last Modified:||04 Jul 2012 09:05|
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