NON DIFFERENTIALBE PERTURBED NEWTON’s METHOD FOR FUNCTIONS WITH VALUES IN A CONE

Abstract

This paper deals with variational inclusions of the form 0 ∈ f (x) + g(x) − K where f is smooth function from a reflexive Banach space X into a Banach space Y , g is a Lipschitz function from X into Y and K is a nonempty closed convex cone in the space Y . We show that the previous problem can be solved by an extension of the Zincenko’s method which can be seen as a perturbed Newton’s method. Numerical results are given at the end of the paper