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An MHS-type Spectral Conjugate Gradient Method and Its Global Convergence.

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Title: An MHS-type Spectral Conjugate Gradient Method and Its Global Convergence.
Authors: Zhang, Keke1 coco_xidian@163.com, Wang, Chunfeng2 wangchunfeng09@126.com, Yang, Jun2 xysfyangjun@163.com
Source: IAENG International Journal of Applied Mathematics. Jun2026, Vol. 56 Issue 6, p2187-2195. 9p.
Subjects: Conjugate gradient methods, Mathematical optimization, Iterative methods (Mathematics), Mathematical programming, Numerical analysis
Abstract: As a highly effective iterative technique, spectral conjugate gradient method is one of the most crucial classes of algorithms for solving large-scale unconstrained optimization problems. Within the scope of this work, an MHS-type spectral conjugate gradient method is developed by integrating the MHS conjugate gradient method with the classical spectral conjugate gradient method. The new search direction fulfills the sufficient descent property without imposing additional line search constraints. Furthermore, under some mild assumptions and the Wolfe line search conditions, we have proven the method is globally convergent. The numerical experimental results demonstrate that the MHS-type spectral conjugate gradient method exhibits favorable and competitive computational performance when addressing large-scale unconstrained optimization problems. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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: An MHS-type Spectral Conjugate Gradient Method and Its Global Convergence.
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Keke%22">Zhang, Keke</searchLink><relatesTo>1</relatesTo><i> coco_xidian@163.com</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Chunfeng%22">Wang, Chunfeng</searchLink><relatesTo>2</relatesTo><i> wangchunfeng09@126.com</i><br /><searchLink fieldCode="AR" term="%22Yang%2C+Jun%22">Yang, Jun</searchLink><relatesTo>2</relatesTo><i> xysfyangjun@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jun2026, Vol. 56 Issue 6, p2187-2195. 9p.
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  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="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+programming%22">Mathematical programming</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: As a highly effective iterative technique, spectral conjugate gradient method is one of the most crucial classes of algorithms for solving large-scale unconstrained optimization problems. Within the scope of this work, an MHS-type spectral conjugate gradient method is developed by integrating the MHS conjugate gradient method with the classical spectral conjugate gradient method. The new search direction fulfills the sufficient descent property without imposing additional line search constraints. Furthermore, under some mild assumptions and the Wolfe line search conditions, we have proven the method is globally convergent. The numerical experimental results demonstrate that the MHS-type spectral conjugate gradient method exhibits favorable and competitive computational performance when addressing large-scale unconstrained optimization problems. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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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        Text: English
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        PageCount: 9
        StartPage: 2187
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      – SubjectFull: Conjugate gradient methods
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
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      – SubjectFull: Mathematical programming
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      – SubjectFull: Numerical analysis
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      – TitleFull: An MHS-type Spectral Conjugate Gradient Method and Its Global Convergence.
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            NameFull: Zhang, Keke
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              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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