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Inexact Newton's method to nonlinear functions with values in a cone (1510.01947v2)
Published 7 Oct 2015 in math.NA
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 \alpha-theorem for inexact Newton's method is obtained.