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**1 - 3**of**3**### A robust semi-local convergence analysis of Newton's . . .

- JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
, 2015

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

, 2015

"... 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 ..."

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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.