# Global convergence in a hybrid conjugate gradient projection method for finding solutions of constrained nonlinear equations with applications

## TL;DR

This paper introduces a new method for solving constrained nonlinear equations that uses less memory and performs better than existing methods on benchmark problems.

## Contribution

A hybrid conjugate gradient projection method with global convergence and improved performance on constrained nonlinear equations.

## Key findings

- The method achieves global convergence under reasonable assumptions.
- It outperforms existing methods on 75.71% to 86.43% of benchmark problems in efficiency metrics.
- Successfully applied to sparse signal restoration problems.

## Abstract

In this paper, a hybrid conjugate gradient projection method for finding solutions of constrained nonlinear equations is proposed by integrating both hyperplane projection and hybrid techniques. The key features of this method are as follows: (1) It is characterized by a low storage requirement and relies solely on function values; (2) The designed search direction ensures the sufficient descent property without the need for line search approaches; (3) Under certain reasonable assumptions, the global convergence of the method is established; (4) Experimental results demonstrate that the proposed method outperforms the two existing methods about 75.71%, 85.36%, and 86.43% of benchmark problems in terms of CPU time, the number of function evaluations, and iterations. Furthermore, it is applied to successfully solve the sparse signal restoration problems.