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arXiv · 1510.01947

Inexact Newton's method to nonlinear functions with values in a cone

O. P. Ferreira·G. N. Silva
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Abstract

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

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O. P. Ferreira, G. N. Silva. 2016-04-21. Inexact Newton's method to nonlinear functions with values in a cone. https://arxiv.org/abs/1510.01947

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