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Volume 19, Issue 5
Convergence of Nonlinear Conjugate Gradient Methods

Yu-Hong Dai

J. Comp. Math., 19 (2001), pp. 539-548.

Published online: 2001-10

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  • Abstract

This paper proves that a simplified Armijo-type line search can ensure the global convergences of the Fletcher-Reeves method and the Polak-Ribiére-Polyak method for unconstrained optimization. Although it seems not possible to verify that the PRP method using the generalized Armijo line search converges globally for generally problems, it can be shown that in this case the PRP method always solves uniformly convex problems.

  • Keywords

Unconstrained optimization, Conjugate gradient, (generalized) Line search, Global convergence.

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-539, author = { , Yu-Hong Dai}, title = {Convergence of Nonlinear Conjugate Gradient Methods}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {5}, pages = {539--548}, abstract = {

This paper proves that a simplified Armijo-type line search can ensure the global convergences of the Fletcher-Reeves method and the Polak-Ribiére-Polyak method for unconstrained optimization. Although it seems not possible to verify that the PRP method using the generalized Armijo line search converges globally for generally problems, it can be shown that in this case the PRP method always solves uniformly convex problems.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9006.html} }
TY - JOUR T1 - Convergence of Nonlinear Conjugate Gradient Methods AU - , Yu-Hong Dai JO - Journal of Computational Mathematics VL - 5 SP - 539 EP - 548 PY - 2001 DA - 2001/10 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9006.html KW - Unconstrained optimization, Conjugate gradient, (generalized) Line search, Global convergence. AB -

This paper proves that a simplified Armijo-type line search can ensure the global convergences of the Fletcher-Reeves method and the Polak-Ribiére-Polyak method for unconstrained optimization. Although it seems not possible to verify that the PRP method using the generalized Armijo line search converges globally for generally problems, it can be shown that in this case the PRP method always solves uniformly convex problems.

, Yu-Hong Dai. (2001). Convergence of Nonlinear Conjugate Gradient Methods. Journal of Computational Mathematics. 19 (5). 539-548. doi:
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