208
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Some superlinearly convergent inexact generalized Newton method for solving nonsmooth equations

Pages 405-417 | Received 23 Jun 2010, Accepted 17 Sep 2010, Published online: 26 Nov 2010
 

Abstract

This paper presents an inexact generalized Newton method for solving the nonlinear equation F(x)=0, where F is locally Lipschitz continuous. The method with backtracking is globally and superlinearly convergent under some mild assumptions on F. The first proposed algorithm is a substantial extension of the well-known inexact Newton method to nonsmooth case based on Pu and Tian [Globally convergent inexact generalized Newton's methods for nonsmooth equations, J. Comput. Appl. Math. 138 (2002), pp. 37–49] approach. Moreover, a hybrid method with Armijo line search, which is globally and quadratically convergent, is also presented. The presented results of numerical experiments are promising and confirm the theoretical properties of introduced methods.

Mathematics Subject Classification :

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,330.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.