The Mathematical Institute, University of Oxford, Eprints Archive

Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients

Cartis, C and Gould, N. I. M. and Toint, Ph. L. (2014) Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients. Technical Report. Not Specified. (Submitted)

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Abstract

The worst-case behaviour of a general class of regularization algorithms is considered in the case where only objective function values and associated gradient vectors are evaluated. Upper bounds are derived on the number of such evaluations that are needed for the algorithm to produce an approximate first-order critical point whose accuracy is within a user-defined threshold. The analysis covers the entire range of meaningful powers in the regularization term as well as for the H¨older exponent for the gradient. The resulting complexity bounds vary according to the regularization power and the assumed Hölder exponent, recovering known results when available

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1874
Deposited By: Helen Taylor
Deposited On:20 Dec 2014 09:50
Last Modified:01 Jul 2015 15:17

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