A perturbed version of an inexact generalized Newton method for solving nonsmooth equations

In this paper, we present the combination of the inexact Newton method and the generalized Newton method for solving nonsmooth equations F(x) = 0, characterizing the local convergence in terms of the perturbations and residuals. We assume that both iteration matrices taken from the B-differential and vectors F(x((k))) are perturbed at each step. Some results are motivated by the approach of Catinas regarding to smooth equations. We study the conditions, which determine admissible magnitude of perturbations to preserve the convergence of method. Finally, the utility of these results is considered based on some variant of the perturbed inexact generalized Newton method for solving some general optimization problems.