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

Coralia Cartis (coralia.cartis***at***maths.ox.ac.uk)
Nick Gould (nick.gould***at***stfc.ac.uk)
Philippe Toint (philippe.toint***at***unamur.be)

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 ifor the Hölder exponent for the gradient. The resulting complexity bounds vary according to the regularization power and the assumed Hölder exponent, recovering known results when available.

Keywords: Nonlinear optimization, complexity, regularization methods

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Report naXys 12-2014, University of Namur, Namur, Belgium

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Entry Submitted: 11/25/2014
Entry Accepted: 11/25/2014
Entry Last Modified: 06/28/2015

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