Inexact Newton method with feasible inexact projections for solving constrained smooth and nonsmooth equations

Abstract

We herein propose a new method that combines the inexact Newton method with a procedure to obtain a feasible inexact projection for solving constrained smooth and nonsmooth equations. Local convergence theorems are established under the assumption of smoothness or semi-smoothness of a function that defines the equations and the regularity of the solution. In particular, we demonstrate that a sequence generated by the method converges to a solution with a linear, superlinear, or quadratic rate, under suitable conditions. Moreover, some numerical experiments are reported to illustrate the practical behavior of the proposed method.