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Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization.

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Title: Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization.
Authors: Kobayashi, Hiroshi1 (AUTHOR), Narushima, Yasushi2 (AUTHOR) narushima@ynu.ac.jp, Yabe, Hiroshi3 (AUTHOR)
Source: Optimization Methods & Software. December 2017, Vol. 32 Issue 6, p1313-1329. 17p.
Subjects: Conjugate gradient methods, Secant function, Trigonometric functions, Number theory, Mathematical optimization
Abstract: The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given. [ABSTRACT FROM PUBLISHER]
Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd 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.)
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  Data: Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization.
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  Data: <searchLink fieldCode="AR" term="%22Kobayashi%2C+Hiroshi%22">Kobayashi, Hiroshi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Narushima%2C+Yasushi%22">Narushima, Yasushi</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> narushima@ynu.ac.jp</i><br /><searchLink fieldCode="AR" term="%22Yabe%2C+Hiroshi%22">Yabe, Hiroshi</searchLink><relatesTo>3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Optimization+Methods+%26+Software%22">Optimization Methods & Software</searchLink>. December 2017, Vol. 32 Issue 6, p1313-1329. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Conjugate+gradient+methods%22">Conjugate gradient methods</searchLink><br /><searchLink fieldCode="DE" term="%22Secant+function%22">Secant function</searchLink><br /><searchLink fieldCode="DE" term="%22Trigonometric+functions%22">Trigonometric functions</searchLink><br /><searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink>
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  Label: Abstract
  Group: Ab
  Data: The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given. [ABSTRACT FROM PUBLISHER]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd 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.)
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        Value: 10.1080/10556788.2017.1338288
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        Text: English
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        PageCount: 17
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      – SubjectFull: Conjugate gradient methods
        Type: general
      – SubjectFull: Secant function
        Type: general
      – SubjectFull: Trigonometric functions
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      – SubjectFull: Number theory
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      – SubjectFull: Mathematical optimization
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              Text: December 2017
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