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

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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
On Efficiently Combining Limited-Memory and Trust-Region Techniques
Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-1836-4200
Tencent, Beijing, China.
Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, Beijing, China.
2017 (English)In: Mathematical Programming Computation, ISSN 1867-2949, E-ISSN 1867-2957, Vol. 9, no 1, 101-134 p.Article in journal (Refereed) Published
Abstract [en]

Limited-memory quasi-Newton methods and trust-region methods represent two efficient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited-memory methods are usually combined with a line search. We show how to efficiently combine limited-memory and trust-region techniques. One of our approaches is based on the eigenvalue decomposition of the limited-memory quasi-Newton approximation of the Hessian matrix. The decomposition allows for finding a nearly-exact solution to the trust-region subproblem defined by the Euclidean norm with an insignificant computational overhead as compared with the cost of computing the quasi-Newton direction in line-search limited-memory methods. The other approach is based on two new eigenvalue-based norms. The advantage of the new norms is that the trust-region subproblem is separable and each of the smaller subproblems is easy to solve. We show that our eigenvalue-based limited-memory trust-region methods are globally convergent. Moreover, we propose improved versions of the existing limited-memory trust-region algorithms. The presented results of numerical experiments demonstrate the efficiency of our approach which is competitive with line-search versions of the L-BFGS method.

Place, publisher, year, edition, pages
2017. Vol. 9, no 1, 101-134 p.
Keyword [en]
Unconstrained Optimization, Large-scale Problems, Limited-Memory Methods, Trust-Region Methods, Shape-Changing Norm, Eigenvalue Decomposition
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-129783DOI: 10.1007/s12532-016-0109-7OAI: oai:DiVA.org:liu-129783DiVA: diva2:943690
Available from: 2016-06-28 Created: 2016-06-28 Last updated: 2017-06-26Bibliographically approved

Open Access in DiVA

fulltext(486 kB)15 downloads
File information
File name FULLTEXT01.pdfFile size 486 kBChecksum SHA-512
6c053878146fb6d0d31ee832224288958977879dcfeb347a0436ac7fb4175f6d3a9e8c743441d7c248103981216db09cadb419c59943a3bc6e3a956059e7b00a
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Burdakov, OlegZikrin, Spartak
By organisation
Optimization Faculty of Science & Engineering
In the same journal
Mathematical Programming Computation
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 15 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 150 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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