Local convergence analysis of Newton's method for solving strongly regular generalized equations

In this paper, we consider Newton's method for solving a generalized equation of the form f(x)+F(x)∋0, where f:Ω→Y is continuously differentiable, X and Y are Banach spaces, Ω⊂X is open, and F:X⇉Y has a nonempty closed graph. We show that, under strong regularity of the equation, the method is locally convergent to a solution with superlinear/quadratic rate. Our analysis, which is based on general majorant condition, enables us to obtain a convergence result under the Lipschitz, Smale's, and Nesterov-Nemirovskii's self-concordant conditions.