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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 8
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Articles

Inexact Newton method for non-linear functions with values in a cone

Pages 1461-1477 | Received 15 Aug 2017, Accepted 13 Jan 2018, Published online: 29 Jan 2018
 

ABSTRACT

The problem of finding a solution of non-linear inclusion problems in Banach space is considered in this paper. Using convex optimization techniques introduced by Robinson (Numer Math. 1972;19:341–347), a robust convergence theorem for the inexact Newton method is proved. As an application, an affine invariant version of Kantorovich’s theorem and Smale’s α-theorem for the inexact Newton method is obtained.

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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by CAPES [Projeto 019/2011]- Cooperação Internacional Brasil-China), CNPq [grant number 471815/2012-8], [grant number 444134/2014-0] and [grant number 305158/2014-7], PRONEX–Optimization (FAPERJ/CNPq) and FAPEG/GO.

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