Inexact Newton Method For Non-Linear Functions With Values In A Cone

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 -theorem for the inexact Newton method is obtained.