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In this paper we study Newton's method for solving generalized equations inBanach spaces. We show that under strong regularity of the generalizedequation, the method is locally convergent to a solution withsuperlinear/quadratic rate. The presented analysis is based on BanachPerturbation Lemma for generalized equation and the classical Lipschitzcondition on the derivative is relaxed by using a general majorant function,which enables obtaining the optimal convergence radius, uniqueness of solutionas well as unifies earlier results pertaining to Newton's method theory.

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