An adaptive regularization algorithm for unconstrained optimization with inexact function and derivatives values

2021/11/28 by Gould, N. I. M., Toint, Ph. L.
#49M37 #90C26 #90C30 #90C56 #F.2.2 #FOS: Mathematics #G.1.6 #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2111.14098

Abstract

An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In comparison with a similar algorithm proposed in Cartis, Gould, Toint (2021), its distinguishing feature is that it is based on controlling the relative error between the model and objective values. A sharp evaluation complexity complexity bound is derived for the new algorithm.

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