View in EDS

Convergence of Conjugate Gradient Methods with a Closed-Form Stepsize Formula.

Saved in:
Bibliographic Details
Title: Convergence of Conjugate Gradient Methods with a Closed-Form Stepsize Formula.
Authors: Labat, C.1, Idier, J.1 Jerome.Idier@irccyn.ec-nantes.fr
Source: Journal of Optimization Theory & Applications. Jan2008, Vol. 136 Issue 1, p43-60. 18p. 1 Chart.
Subjects: Conjugate gradient methods, Mathematical optimization, Stochastic convergence, Approximation theory, Maxima & minima, Convex domains, Convex surfaces, Iterative methods (Mathematics), Numerical solutions to equations
Abstract: Conjugate gradient methods are efficient methods for minimizing differentiable objective functions in large dimension spaces. However, converging line search strategies are usually not easy to choose, nor to implement. Sun and colleagues (Ann. Oper. Res. 103:161-173, 2001; J. Comput. Appl.Math. 146:37-45, 2002) introduced a simple stepsize formula. However, the associated convergence domain happens to be overrestrictive, since it precludes the optimal stepsize in the convex quadratic case. Here, we identify this stepsize formula with one iteration of the Weiszfeld algorithm in the scalar case. More generally, we propose to make use of a finite number of iterates of such an algorithm to compute the stepsize. In this framework, we establish a new convergence domain, that incorporates the optimal stepsize in the convex quadratic case. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 29360382
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Convergence of Conjugate Gradient Methods with a Closed-Form Stepsize Formula.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Labat%2C+C%2E%22">Labat, C.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Idier%2C+J%2E%22">Idier, J.</searchLink><relatesTo>1</relatesTo><i> Jerome.Idier@irccyn.ec-nantes.fr</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Journal+of+Optimization+Theory+%26+Applications%22">Journal of Optimization Theory & Applications</searchLink>. Jan2008, Vol. 136 Issue 1, p43-60. 18p. 1 Chart.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Conjugate+gradient+methods%22">Conjugate gradient methods</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+convergence%22">Stochastic convergence</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Maxima+%26+minima%22">Maxima & minima</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+domains%22">Convex domains</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+surfaces%22">Convex surfaces</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+equations%22">Numerical solutions to equations</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Conjugate gradient methods are efficient methods for minimizing differentiable objective functions in large dimension spaces. However, converging line search strategies are usually not easy to choose, nor to implement. Sun and colleagues (Ann. Oper. Res. 103:161-173, 2001; J. Comput. Appl.Math. 146:37-45, 2002) introduced a simple stepsize formula. However, the associated convergence domain happens to be overrestrictive, since it precludes the optimal stepsize in the convex quadratic case. Here, we identify this stepsize formula with one iteration of the Weiszfeld algorithm in the scalar case. More generally, we propose to make use of a finite number of iterates of such an algorithm to compute the stepsize. In this framework, we establish a new convergence domain, that incorporates the optimal stepsize in the convex quadratic case. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=29360382
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s10957-007-9306-x
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
        StartPage: 43
    Subjects:
      – SubjectFull: Conjugate gradient methods
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Stochastic convergence
        Type: general
      – SubjectFull: Approximation theory
        Type: general
      – SubjectFull: Maxima & minima
        Type: general
      – SubjectFull: Convex domains
        Type: general
      – SubjectFull: Convex surfaces
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Numerical solutions to equations
        Type: general
    Titles:
      – TitleFull: Convergence of Conjugate Gradient Methods with a Closed-Form Stepsize Formula.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Labat, C.
      – PersonEntity:
          Name:
            NameFull: Idier, J.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Text: Jan2008
              Type: published
              Y: 2008
          Identifiers:
            – Type: issn-print
              Value: 00223239
          Numbering:
            – Type: volume
              Value: 136
            – Type: issue
              Value: 1
          Titles:
            – TitleFull: Journal of Optimization Theory & Applications
              Type: main
ResultId 1