A family of Newton methods for nonsmooth constrained systems with nonisolated solutions

We propose a new family of Newton‐type methods for the solution of constrained systems of equations. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, local, quadratic convergence to a solution of the system of equations can be established. We show that as particular instances of the method we obtain inexact versions of both a recently introduced LP‐based Newton method and of a Levenberg‐Marquardt algorithm for the solution of systems with nonisolated solutions, and improve on corresponding existing results.