An efficient hybrid conjugate gradient method for unconstrained optimization. (4th July 2022)

• Record Type: Journal Article
• Authors: Ibrahim, Abdulkarim Hassan; Kumam, Poom; Kamandi, Ahmad; Abubakar, Auwal Bala
• Is Part Of: Optimization methods and software. Volume 37:Number 4(2022)
• Page Start: 1370
• Page End: 1383
• Publication Date: 2022-07-04
• Subjects: Unconstrained optimization -- conjugate gradient method -- hybrid conjugate gradient method -- Dai–Liao conjugacy -- Quasi-Newton direction -- CUTEst; 65K05 -- 90C30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2021.1998490
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, we propose a hybrid conjugate gradient method for unconstrained optimization, obtained by a convex combination of the LS and KMD conjugate gradient parameters. A favourite property of the proposed method is that the search direction satisfies the Dai–Liao conjugacy condition and the quasi-Newton direction. In addition, this property does not depend on the line search. Under a modified strong Wolfe line search, we establish the global convergence of the method. Numerical comparison using a set of 109 unconstrained optimization test problems from the CUTEst library show that the proposed method outperforms the Liu–Storey and Hager–Zhang conjugate gradient methods.