Convergence of a generalized Newton and an inexact generalized Newton algorithms for solving nonlinear equations with nondifferentiable terms

In this paper, we consider two versions of the Newton-type method for solving a nonlinear equations with nondifferentiable terms, which uses as iteration matrices, any matrix from B-differential of semismooth terms. Local and global convergence theorems for the generalized Newton and inexact generalized Newton method are proved. Linear convergence of the algorithms is obtained under very mild assumptions. The superlinear convergence holds under some conditions imposed on both terms of equation. Some numerical results indicate that both algorithms works quite well in practice.