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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COPYRIGHT: © Global Science Press

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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} }
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