Local convergence of Newton’s method for subanalytic variational inclusions

摘要

This paper concerns variational inclusions of the form $0 in f(x) + F(x)$ where f is a single locally Lipschitz subanalytic function and F is a set-valued map acting in Banach spaces. We prove the existence and the convergence of a sequence (x k ) satisfying $0 in f(x_k)+Delta f(x_k)(x_{k+1}-x_k)+F(x_{k+1})$ where $Delta f(x_k)$ lies to $partial f(x_k)$ which is the Clarke Jacobian of f at the point x k .