New adaptive stepsize selections in gradient methods

Giacomo Frassoldati; Luca Zanni; Gaetano Zanghirati

doi:10.3934/jimo.2008.4.299

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2008, Volume 4, Issue 2: 299-312. Doi: 10.3934/jimo.2008.4.299

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New adaptive stepsize selections in gradient methods

1.
Department of Pure and Applied Mathematics, University of Modena and Reggio Emilia, via Campi 213/b, I-41100 Modena
2.
University of Ferrara, Department of Mathematics and Mathematics-for-Technology Center, Scientific-Technological Campus, Building B, via Saragat, 1, I-44100 Ferrara

Received: February 28, 2007

Revised: September 30, 2007

Published: March 2008

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Abstract

This paper deals with gradient methods for minimizing $n$-dimen-sional strictly convex quadratic functions. Two new adaptive stepsize selection rules are presented and some key properties are proved. Practical insights on the effectiveness of the proposed techniques are given by a numerical comparison with the Barzilai-Borwein (BB) method, the cyclic/adaptive BB methods and two recent monotone gradient methods.

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Mathematics Subject Classification: Primary: 65K05, 65B99; Secondary: 90C20.

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