@Article{JCM-37-6,
author = {Oleg, Burdakov and Yuhong, Dai and Na, Huang},
title = {Stabilized Barzilai-Borwein Method},
journal = {Journal of Computational Mathematics},
year = {2019},
volume = {37},
number = {6},
pages = {916--936},
abstract = {<p style="text-align: justify;">The Barzilai-Borwein (BB) method is a popular and efficient tool for solving large-scale
unconstrained optimization problems. Its search direction is the same as the steepest
descent (Cauchy) method, but its step size rule is different. Owing to this, it converges
much faster than the Cauchy method. A feature of the BB method is that it may generate
too long steps, which throw the iterates too far away from the solution. Moreover, it
may not converge, even when the objective function is strongly convex. In this paper, a
stabilization technique is introduced. It consists in bounding the distance between each
pair of successive iterates, which often allows for decreasing the number of BB iterations.
When the BB method does not converge, our simple modification of this method makes
it convergent. For strongly convex functions with Lipschits gradients, we prove its global
convergence, despite the fact that no line search is involved, and only gradient values are
used. Since the number of stabilization steps is proved to be finite, the stabilized version
inherits the fast local convergence of the BB method. The presented results of extensive
numerical experiments show that our stabilization technique often allows the BB method
to solve problems in a fewer iterations, or even to solve problems where the latter fails.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1911-m2019-0171},
url = {https://global-sci.com/article/84452/stabilized-barzilai-borwein-method}
}