Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations

M Koorapetse,P Kaelo

doi:10.1186/s42787-019-0066-1

Abstract

In this paper, we propose a self adaptive spectral conjugate gradient-based projection method for systems of nonlinear monotone equations. Based on its modest memory requirement and its efficiency, the method is suitable for solving large-scale equations. We show that the method satisfies the descent condition F_{k}^{T}d_{k}leq -c|F_{k}|^{2}, c>0, and also prove its global convergence. The method is compared to other existing methods on a set of benchmark test problems and results show that the method is very efficient and therefore promising.

Highlights

Due to their modest memory requirements, conjugate gradient-based projection methods are suitable for solving large-scale nonlinear monotone equations (1)
In this paper, we focus on solving large-scale nonlinear system of equations F(x) = 0, (1)where F : Rn → Rn is continuous and monotone
Nonlinear monotone equations arise in many practical applications, for example, chemical equilibrium systems [1], economic equilibrium problems [2], and some monotone variational inequality problems [3]

Summary

Introduction

Due to their modest memory requirements, conjugate gradient-based projection methods are suitable for solving large-scale nonlinear monotone equations (1). (2020) 28:4 gradient-based projection methods generate a sequence {xk} by exploring the monotonicity of the function F. Following Solodov and Svaiter [10], a lot of work has been done, and continues to be done, to come up with a number of conjugate gradient-based projection methods for nonlinear monotone equations.

Results

Conclusion