Extension of Newton's method to nonlinear functions with values in a cone

AbstractWe show how Newton's method may be extended, using convex optimization techniques, to solve problems of the form $$Find \bar x such that f(\bar x) \in K$$ , whereK is a nonempty closed convex cone in a Banach spaceY, andf is a function from a reflexive Banach spaceX intoY. A generalization of the Kantorovich theorem is proved, giving convergence results and error bounds for this method.