# American Institute of Mathematical Sciences

April  2008, 4(2): 299-312. doi: 10.3934/jimo.2008.4.299

## 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, Italy, Italy 2 University of Ferrara, Department of Mathematics and Mathematics-for-Technology Center, Scientific-Technological Campus, Building B, via Saragat, 1, I-44100 Ferrara, Italy

Received  March 2007 Revised  October 2007 Published  April 2008

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.
Citation: Giacomo Frassoldati, Luca Zanni, Gaetano Zanghirati. New adaptive stepsize selections in gradient methods. Journal of Industrial & Management Optimization, 2008, 4 (2) : 299-312. doi: 10.3934/jimo.2008.4.299
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