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

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

0.00 Avg rating0 Votes
Article ID: iaor20134155
Volume: 56
Issue: 4
Start Page Number: 1791
End Page Number: 1815
Publication Date: Aug 2013
Journal: Journal of Global Optimization
Authors: , ,
Keywords: approximation, global optimization
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.

Reviews

Required fields are marked *. Your email address will not be published.