On the global convergent of an inexact quasi-Newton conditional gradient method for constrained nonlinear systems

TL;DR

This paper introduces a globally convergent method for constrained nonlinear systems that combines a Newton conditional gradient approach with a derivative-free linesearch, supported by theoretical analysis and preliminary numerical results.

Contribution

It proposes a novel combination of Newton conditional gradient and derivative-free linesearch methods with proven global convergence for constrained nonlinear systems.

Findings

Method demonstrates global convergence under certain conditions.

Preliminary experiments show promising performance.

Combines efficiency of Newton methods with flexibility of linesearch.

Abstract

In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global convergence analysis of the proposed method is established under suitable conditions, and some preliminary numerical experiments are given to illustrate its performance.