# An Inexact Newton-like conditional gradient method for constrained nonlinear systems

## TL;DR

This paper introduces an inexact Newton-like conditional gradient method for solving constrained nonlinear systems, establishing local convergence and rate under general conditions, with applications to Holder-like and Smale functions, supported by numerical experiments.

## Contribution

It presents a novel inexact Newton-like conditional gradient method with convergence analysis for constrained nonlinear systems, applicable to a broad class of functions including analytic ones.

## Key findings

- Method converges locally under general conditions.
- Applicable to functions with Holder-like derivatives and Smale conditions.
- Numerical experiments demonstrate effectiveness on medium and large problems.

## Abstract

In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of the new method as well as results on its rate are established by using a general majorant condition. Two applications of such condition are provided: one is for functions whose the derivative satisfies Holder-like condition and the other is for functions that satisfies a Smale condition, which includes a substantial class of analytic functions. Some preliminaries numerical experiments illustrating the applicability of the proposed method for medium and large problems are also presented.