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

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.

15 pages, 0 figure. arXiv admin note: text overlap with arXiv:1403.2462

Cited by in corpus (1)

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