A positive barzilai-borwein-like stepsize and an extension for symmetric linear systems

Yu Hong Dai*, Mehiddin Al-Baali, Xiaoqi Yang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

26 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationNumerical Analysis and Optimization, NAO-III 2014
EditorsMehiddin Al-Baali, Lucio Grandinetti, Anton Purnama
PublisherSpringer New York LLC
Pages59-75
Number of pages17
ISBN (Print)9783319176888
DOIs
Publication statusPublished - 2015
Event3rd International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOIII-2014 - Muscat, Oman
Duration: Jan 5 2014Jan 9 2014

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume134
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other3rd International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOIII-2014
Country/TerritoryOman
CityMuscat
Period1/5/141/9/14

Keywords

  • Barzilai and Borwein gradient method
  • Condition number
  • Quadratic function
  • R-superlinear convergence
  • Unconstrained optimization

ASJC Scopus subject areas

  • General Mathematics

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