Volume 14, Issue 2
A Linear Hybridization of Dai-Yuan and Hestenes-Stiefel Conjugate Gradient Method for Unconstrained Optimization

Sindhu NarayananP. Kaelo

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 527-539.

Published online: 2021-01

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  • Abstract

Conjugate gradient methods are interesting iterative methods that solve large scale unconstrained optimization problems. A lot of recent research has thus focussed on developing a number of conjugate gradient methods that are more effective. In this paper, we propose another hybrid conjugate gradient method as a linear combination of Dai-Yuan (DY) method and the Hestenes-Stiefel (HS) method. The sufficient descent condition and the global convergence of this method are established using the generalized Wolfe line search conditions. Compared to the other conjugate gradient methods, the proposed method gives good numerical results and is effective.

  • Keywords

Unconstrained optimization, conjugate gradient method, global convergence.

  • AMS Subject Headings

90C06, 90C30, 65K05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-14-527, author = {Narayanan , Sindhu and Kaelo , P.}, title = {A Linear Hybridization of Dai-Yuan and Hestenes-Stiefel Conjugate Gradient Method for Unconstrained Optimization}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2021}, volume = {14}, number = {2}, pages = {527--539}, abstract = {

Conjugate gradient methods are interesting iterative methods that solve large scale unconstrained optimization problems. A lot of recent research has thus focussed on developing a number of conjugate gradient methods that are more effective. In this paper, we propose another hybrid conjugate gradient method as a linear combination of Dai-Yuan (DY) method and the Hestenes-Stiefel (HS) method. The sufficient descent condition and the global convergence of this method are established using the generalized Wolfe line search conditions. Compared to the other conjugate gradient methods, the proposed method gives good numerical results and is effective.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0056}, url = {http://global-sci.org/intro/article_detail/nmtma/18610.html} }
TY - JOUR T1 - A Linear Hybridization of Dai-Yuan and Hestenes-Stiefel Conjugate Gradient Method for Unconstrained Optimization AU - Narayanan , Sindhu AU - Kaelo , P. JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 527 EP - 539 PY - 2021 DA - 2021/01 SN - 14 DO - http://doi.org/10.4208/nmtma.OA-2020-0056 UR - https://global-sci.org/intro/article_detail/nmtma/18610.html KW - Unconstrained optimization, conjugate gradient method, global convergence. AB -

Conjugate gradient methods are interesting iterative methods that solve large scale unconstrained optimization problems. A lot of recent research has thus focussed on developing a number of conjugate gradient methods that are more effective. In this paper, we propose another hybrid conjugate gradient method as a linear combination of Dai-Yuan (DY) method and the Hestenes-Stiefel (HS) method. The sufficient descent condition and the global convergence of this method are established using the generalized Wolfe line search conditions. Compared to the other conjugate gradient methods, the proposed method gives good numerical results and is effective.

Sindhu Narayanan & P. Kaelo. (2021). A Linear Hybridization of Dai-Yuan and Hestenes-Stiefel Conjugate Gradient Method for Unconstrained Optimization. Numerical Mathematics: Theory, Methods and Applications. 14 (2). 527-539. doi:10.4208/nmtma.OA-2020-0056
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