Year: 2021
Author: Harry Oviedo, Oscar Dalmau, Rafael Herrera
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 3 : pp. 375–391
Abstract
In this work we introduce two new Barzilai and Borwein-like steps sizes for the classical gradient method for strictly convex quadratic optimization problems. The proposed step sizes employ second-order information in order to obtain faster gradient-type methods. Both step sizes are derived from two unconstrained optimization models that involve approximate information of the Hessian of the objective function. A convergence analysis of the proposed algorithm is provided. Some numerical experiments are performed in order to compare the efficiency and effectiveness of the proposed methods with similar methods in the literature. Experimentally, it is observed that our proposals accelerate the gradient method at nearly no extra computational cost, which makes our proposal a good alternative to solve large-scale problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2001-m2018-0205
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 3 : pp. 375–391
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Gradient methods Convex quadratic optimization Hessian spectral properties Steplength selection.
Author Details
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