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

Yu Hong Dai, Mehiddin Al-Baali, Xiaoqi Yang

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

5 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 publicationSpringer Proceedings in Mathematics and Statistics
PublisherSpringer New York LLC
Pages59-75
Number of pages17
Volume134
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

Other

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

Fingerprint

Steepest Descent Method
Superlinear Convergence
Gradient Method
Strictly Convex
Quadratic Function
Convex function
Linear Systems
Gradient
Context

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Dai, Y. H., Al-Baali, M., & Yang, X. (2015). A positive barzilai-borwein-like stepsize and an extension for symmetric linear systems. In Springer Proceedings in Mathematics and Statistics (Vol. 134, pp. 59-75). Springer New York LLC. https://doi.org/10.1007/978-3-319-17689-5_3

A positive barzilai-borwein-like stepsize and an extension for symmetric linear systems. / Dai, Yu Hong; Al-Baali, Mehiddin; Yang, Xiaoqi.

Springer Proceedings in Mathematics and Statistics. Vol. 134 Springer New York LLC, 2015. p. 59-75.

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

Dai, YH, Al-Baali, M & Yang, X 2015, A positive barzilai-borwein-like stepsize and an extension for symmetric linear systems. in Springer Proceedings in Mathematics and Statistics. vol. 134, Springer New York LLC, pp. 59-75, 3rd International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOIII-2014, Muscat, Oman, 1/5/14. https://doi.org/10.1007/978-3-319-17689-5_3
Dai YH, Al-Baali M, Yang X. A positive barzilai-borwein-like stepsize and an extension for symmetric linear systems. In Springer Proceedings in Mathematics and Statistics. Vol. 134. Springer New York LLC. 2015. p. 59-75 https://doi.org/10.1007/978-3-319-17689-5_3
Dai, Yu Hong ; Al-Baali, Mehiddin ; Yang, Xiaoqi. / A positive barzilai-borwein-like stepsize and an extension for symmetric linear systems. Springer Proceedings in Mathematics and Statistics. Vol. 134 Springer New York LLC, 2015. pp. 59-75
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