Two Generalized Derivative-free Methods to Solve Large Scale Nonlinear Equations with Convex Constraints

TL;DR

This paper introduces two derivative-free algorithms for solving large-scale nonlinear equations with convex constraints, demonstrating their convergence properties and efficiency through numerical experiments.

Contribution

It presents two novel derivative-free methods based on conjugate gradient techniques for large-scale constrained nonlinear equations, with proven convergence properties.

Findings

Algorithms satisfy the sufficient descent condition

Global convergence of one method independent of Lipschitz continuity

Numerical results confirm the algorithms' efficiency

Abstract

In this work, we propose two derivative-free methods to address the problem of large-scale nonlinear equations with convex constraints. These algorithms satisfy the sufficient descent condition. The search directions can be considered generalizations of the Modified Optimal Perry conjugate gradient method and the conjugate gradient projection method or the Spectral Modified Optimal Perry conjugate gradient method and the Spectral Conjugate Gradient Projection method. The global convergence of the former does not depend on the Lipschitz continuity of G. In contrast, the latter's global convergence depends on the Lipschitz continuity of G. The numerical results show the efficiency of the algorithms.