Expanding the Applicability of the Kantorovich’s Theorem for Solving Generalized Equations Using Newton’s Method

Abstract

In this paper we consider the Kantorovich’s theorem for solving generalized equations F(x) + Q(x) ? 0 using Newton’s method, where F is a Fréchet differentiable function and Q is a set-valued and maximal monotone function acting between Hilbert spaces. We used our new idea of restricted convergence domains to obtain better location about where the iterates are located leading to a tighter convergence analysis than in the earlier studies and under the same or less computational cost of the majorant functions involved. © 2016, Springer India Pvt. Ltd.