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Volume 20, Issue 3
Globally Convergent Inexact Generalized Newton Methods with Decreasing Norm of the Gradient

Ding-Guo Pu

J. Comp. Math., 20 (2002), pp. 289-300.

Published online: 2002-06

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  • Abstract

In this paper, motivated by the Martinez and Qi methods [1], we propose one type of globally convergent inexact generalized Newton methods to solve unconstrained optimization problems in which the objective functions are not twice differentiable, but have LC gradient. They make the norm of the gradient decreasing. These methods are implementable and globally convergent. We prove that the algorithms have superlinear convergence rates under some mild conditions.
The methods may also be used to solve nonsmooth equations.

  • Keywords

Nonsmooth optimization, Inexact Newton method, Generalized Newton method, Global convergence, superlinear rate.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-20-289, author = {Pu , Ding-Guo}, title = {Globally Convergent Inexact Generalized Newton Methods with Decreasing Norm of the Gradient}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {3}, pages = {289--300}, abstract = {

In this paper, motivated by the Martinez and Qi methods [1], we propose one type of globally convergent inexact generalized Newton methods to solve unconstrained optimization problems in which the objective functions are not twice differentiable, but have LC gradient. They make the norm of the gradient decreasing. These methods are implementable and globally convergent. We prove that the algorithms have superlinear convergence rates under some mild conditions.
The methods may also be used to solve nonsmooth equations.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8918.html} }
TY - JOUR T1 - Globally Convergent Inexact Generalized Newton Methods with Decreasing Norm of the Gradient AU - Pu , Ding-Guo JO - Journal of Computational Mathematics VL - 3 SP - 289 EP - 300 PY - 2002 DA - 2002/06 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8918.html KW - Nonsmooth optimization, Inexact Newton method, Generalized Newton method, Global convergence, superlinear rate. AB -

In this paper, motivated by the Martinez and Qi methods [1], we propose one type of globally convergent inexact generalized Newton methods to solve unconstrained optimization problems in which the objective functions are not twice differentiable, but have LC gradient. They make the norm of the gradient decreasing. These methods are implementable and globally convergent. We prove that the algorithms have superlinear convergence rates under some mild conditions.
The methods may also be used to solve nonsmooth equations.

Pu , Ding-Guo. (2002). Globally Convergent Inexact Generalized Newton Methods with Decreasing Norm of the Gradient. Journal of Computational Mathematics. 20 (3). 289-300. doi:
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