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

Ding Guo Pu

DOI:

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[l], 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 mile conditions.\par The methods may also be used to solve nonsmooth epuations.

  • Keywords

Nonsmooth optimization Inexact Newton method Generalized Newton method Global convergence Superoinear rate

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@Article{JCM-20-289, author = {}, 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[l], 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 mile conditions.\par The methods may also be used to solve nonsmooth epuations. }, 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 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 KW - Inexact Newton method KW - Generalized Newton method KW - Global convergence KW - Superoinear rate AB - In this paper, motivated by the Martinez and Qi methods[l], 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 mile conditions.\par The methods may also be used to solve nonsmooth epuations.
Ding Guo Pu. (1970). 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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