Another hybrid conjugate gradient method as a convex combination of WYL and CD methods

Guefassa Imane (), Chaib Yacine () and Bechouat Tahar ()
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Guefassa Imane: Laboratory Informatics and Mathematics (LIM), Mohamed Cherif Messaadia University, Souk Ahras, Algeria
Chaib Yacine: Laboratory Informatics and Mathematics (LIM), Mohamed Cherif Messaadia University, Souk Ahras, Algeria
Bechouat Tahar: Laboratory Informatics and Mathematics (LIM), Mohamed Cherif Messaadia University, Souk Ahras, Algeria

Monte Carlo Methods and Applications, 2024, vol. 30, issue 3, 225-234

Abstract: Conjugate gradient (CG) methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems. In this paper, a new hybrid conjugate gradient (CG) method is presented and analyzed for solving unconstrained optimization problems, where the parameter β k \beta_{k} is a convex combination of β k WYL \beta_{k}^{\mathrm{WYL}} and β k CD \beta_{k}^{\mathrm{CD}} . Under the strong Wolfe line search, the new method possesses the sufficient descent condition and the global convergence properties. The preliminary numerical results show the efficiency of our method in comparison with other CG methods. Furthermore, the proposed algorithm HWYLCD was extended to solve the problem of a mode function.

Keywords: Hybrid conjugate gradient method; line search; sufficient descent condition; global convergence; numerical comparisons; mode function; kernel estimator (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1515/mcma-2024-2007

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