A descent modified HS conjugate gradient method with an optimal property

¹ School of Economics and Management, Beijing Jiaotong University, Beijing 100044, P.R. China
² College of Computer and Science Technology, Dongguan University of Technology, Dongguan 523000, P.R. China

^* Corresponding author: 275191090@qq.com

Received: 10 June 2022
Accepted: 16 October 2022

Abstract

In this paper, by minimizing the distance between the CG direction and the direction of the improved Perry conjugate gradient method [Yao et al., Numer. Algorithms 78 (2018) 1255–1269], we propose a descent modified HS conjugate gradient method. A remarkable property of the modified HS method is that it can produce sufficient descent property, which is independent of the line search used. Under suitable conditions, we prove that the modified HS method with the standard Armijo line search is globally convergent for uniformly convex functions and the modified HS+ method with standard Wolfe line search is globally convergent for general nonlinear functions. Extensive numerical experiments show that the proposed method is efficient.