Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/55601
Title: A positive barzilai-borwein-like stepsize and an extension for symmetric linear systems
Authors: Dai, YH
Al-Baali, M
Yang, X 
Keywords: Barzilai and borwein gradient method
Condition number
Quadratic function
R-superlinear convergence
Unconstrained optimization
Issue Date: 2015
Publisher: Springer New York LLC
Source: Springer Proceedings in Mathematics and Statistics, v. 134, p. 59-75 How to cite?
Abstract: The Barzilai and Borwein (BB) gradient method has achieved a lot of attention since it performs much more better than the classical steepest descent method. In this paper, we analyze a positive BB-like gradient stepsize and discuss its possible uses. Specifically, we present an analysis of the positive stepsize for two-dimensional strictly convex quadratic functions and prove the R-superlinear convergence under some assumption. Meanwhile, we extend BB-like methods for solving symmetric linear systems and find that a variant of the positive stepsize is very useful in the context. Some useful discussions on the positive stepsize are also given.
URI: http://hdl.handle.net/10397/55601
ISBN: 9783319176888
ISSN: 2194-1009
DOI: 10.1007/978-3-319-17689-5_3
Appears in Collections:Conference Paper

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