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

Nicholas I. M. Gould(nick.gouldstfc.ac.uk)
Philippe L. Toint(philippe.tointunamur.be)

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 (2022), 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.

Keywords: nonconvex optimization, inexact functions and derivative values, evaluation complexity, adaptive regularization

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

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Entry Submitted: 12/12/2021
Entry Accepted: 12/12/2021
Entry Last Modified: 12/12/2021

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