Title: A new efficient hybrid conjugate gradient method based on LS-DY-HS conjugate gradient parameter

Authors: Nirmalya Kumar Mohanty; Rupaj Kumar Nayak

Addresses: Department of Mathematics, International Institute of Information Technology, Bhubaneswar, Odisha, 751029, India ' Department of Mathematics, International Institute of Information Technology, Bhubaneswar, Odisha, 751029, India

Abstract: A nonlinear conjugate gradient method solves unconstrained optimisation problem based on an efficient line search technique and maintains a decent direction search (in case of a minimisation problem) with the help of conjugate gradient parameter. In this paper, a new hybrid conjugate gradient method based on a hybrid conjugate gradient parameter β_k is proposed. The proposed β_k combines linearly the conjugate gradient parameters of LS, DY and HS method. The present work also discusses the global convergence of the modified algorithm with inexact line search. Moreover, the proposed method is tested on the unconstrained problems from the library CUTEr (Gould et al., 2015) and the results have been compared with the other state of the art algorithms. The results in the numerical experiment show that the proposed hybrid algorithm is efficient.

Keywords: nonlinear conjugate gradient method; unconstrained optimisation; line search; hybrid conjugate gradient parameter; descent property.

DOI: 10.1504/IJMMNO.2020.110702

International Journal of Mathematical Modelling and Numerical Optimisation, 2020 Vol.10 No.4, pp.342 - 364

Received: 19 Jul 2019
Accepted: 19 Jan 2020
Published online: 28 Oct 2020 *

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