liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Stabilized Barzilai-Borwein method
Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-1836-4200
Chinese Academy of Sciences, Beijing, China.
China Agricultural University, Beijing, China.
2019 (English)In: Journal of Computational Mathematics, ISSN 0254-9409, E-ISSN 1991-7139, Vol. 37, no 6, p. 916-936Article in journal (Refereed) Published
Abstract [en]

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 for the steepest descent (Cauchy) method, but its stepsize 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.

Place, publisher, year, edition, pages
Global Science Press, 2019. Vol. 37, no 6, p. 916-936
Keywords [en]
Unconstrained optimization, Spectral algorithms, Stabilization, Convergence analysis.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-162637DOI: 10.4208/jcm.1911-m2019-0171ISI: 000504738100009OAI: oai:DiVA.org:liu-162637DiVA, id: diva2:1377530
Note

Funding agencies:  Visiting Scientist award under the Chinese Academy of Sciences Presidents International Fellowship Initiative; Chinese Natural Science FoundationNational Natural Science Foundation of China [11631013]; National 973 Program of ChinaNational Basic Research 

Available from: 2019-12-12 Created: 2019-12-12 Last updated: 2020-01-09Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Authority records BETA

Burdakov, Oleg

Search in DiVA

By author/editor
Burdakov, Oleg
By organisation
Optimization Faculty of Science & Engineering
In the same journal
Journal of Computational Mathematics
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 8 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf