Newton-Scant method for functions with values in a cone
Résumé
This paper deals with variational inclusions of the form 0 ∈ K − f(x) − g(x) where f is a smooth function from a reflexive Banach space X into a Banach space Y , g is a function from X into Y admitting divided differences and K is a nonempty closed convex cone in the space Y . We show that the previous problem can be solved by a combination of two methods: the Newton and the Secant methods. We show that the order of the semilocal method obtained is equal to (1 + √5)/2. Numerical results are also given to illustrate the convergence at the end of the paper.