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JOURNALS // Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki // Archive

Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2023 Volume 33, Issue 2, Pages 348–364 (Mi vuu854)

MATHEMATICS

A new hybrid conjugate gradient algorithm for unconstrained optimization

Hafaidia Imanea, H. Guebbaia, Al-Baali Mehiddinb, M. Ghiata

a Université 8 Mai 1945 - Guelma
b Sultan Qaboos University

Abstract: It is well known that conjugate gradient methods are useful for solving large-scale unconstrained nonlinear optimization problems. In this paper, we consider combining the best features of two conjugate gradient methods. In particular, we give a new conjugate gradient method, based on the hybridization of the useful DY (Dai-Yuan), and HZ (Hager-Zhang) methods. The hybrid parameters are chosen such that the proposed method satisfies the conjugacy and sufficient descent conditions. It is shown that the new method maintains the global convergence property of the above two methods. The numerical results are described for a set of standard test problems. It is shown that the performance of the proposed method is better than that of the DY and HZ methods in most cases.

Keywords: unconstrained optimization, conjugate gradient methods, conjugacy conditions and sufficient descent conditions.

UDC: 519.6

MSC: 90C30, 90C53

Received: 02.07.2022
Accepted: 17.03.2023

Language: English

DOI: 10.35634/vm230211



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© Steklov Math. Inst. of RAS, 2024