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

TL;DR

This paper introduces a novel inexact Newton method with feasible inexact projections for solving constrained smooth and nonsmooth equations, providing convergence analysis and demonstrating practical effectiveness through numerical experiments.

Contribution

It develops a new combined approach that ensures convergence for constrained equations with smooth or semismooth functions, extending existing methods.

Findings

Convergence to solutions with linear, superlinear, or quadratic rates.

The method performs effectively in numerical experiments.

Theoretical convergence results under regularity and smoothness assumptions.

Abstract

In this paper, we 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. The local convergence theorems are established under the assumption of smoothness or semismoothness of the function that defines the equation and its regularity at the solution. In particular, we show that a sequence generated by the method converges to a solution with linear, superlinear, or quadratic rate, under suitable conditions. Moreover, some numerical experiments are reported to illustrate the practical behavior of the proposed method.