A modified Hager-Zhang conjugate gradient method with optimal choices for solving monotone nonlinear equations. Issue 2 (1st February 2022)

• Record Type: Journal Article
• Authors: Sabi'u, J.; Shah, A.; Waziri, M. Y.
• Is Part Of: International journal of computer mathematics. Volume 99:Issue 2(2022)
• Page Start: 332
• Page End: 354
• Publication Date: 2022-02-01
• Subjects: Conjugate gradient -- monotone equations -- secant equation -- hyperplane -- singular value; 90C30 -- 90C26; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2021.1910814
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : The conjugate gradient method is one of the most robust algorithms to solve large-scale monotone problems due to its limited memory requirements. However, in this article, we used the modified secant equation and proposed two optimal choices for the non-negative constant of the Hager-Zhang (HZ) conjugate gradient method by minimizing the upper bound of the condition number for the HZ search direction matrix. Two algorithms for solving large-scale non-linear monotone equations that incorporate the concept of projection method are provided. Based on monotone and Lipschitz continuous assumptions, we developed the global convergence of the methods. Computational results indicate that the proposed algorithms are effective and efficient.