Local convergence analysis of Newton's method for solving strongly regular generalized equations
Provides a unified theoretical framework for Newton's method convergence analysis, benefiting researchers in optimization and numerical analysis.
This paper proves local superlinear/quadratic convergence of Newton's method for strongly regular generalized equations in Banach spaces, using a majorant function to relax Lipschitz conditions and achieve optimal convergence radius.
In this paper we study Newton's method for solving generalized equations in Banach spaces. We show that under strong regularity of the generalized equation, the method is locally convergent to a solution with superlinear/quadratic rate. The presented analysis is based on Banach Perturbation Lemma for generalized equation and the classical Lipschitz condition on the derivative is relaxed by using a general majorant function, which enables obtaining the optimal convergence radius, uniqueness of solution as well as unifies earlier results pertaining to Newton's method theory.