Authors: Ivanov, Branislav
Milovanović, Gradimir V.
Stanimirović, Predrag S.
Awwal, Aliyu Muhammed
Kazakovtsev, Lev A.
Krutikov, Vladimir N.
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A Modified Dai-Liao Conjugate Gradient Method Based on a Scalar Matrix Approximation of Hessian and Its Application
Journal: Journal of Mathematics
Volume: 2023
First page: 9945581
Editors: Gu, Xian-Ming
Issue Date: 2023
Rank: ~M21
ISSN: 2314-4629
DOI: 10.1155/2023/9945581
Abstract: 
We introduce and investigate proper accelerations of the Dai-Liao (DL) conjugate gradient (CG) family of iterations for solving large-scale unconstrained optimization problems. The improvements are based on appropriate modifications of the CG update parameter in DL conjugate gradient methods. The leading idea is to combine search directions in accelerated gradient descent methods, defined based on the Hessian approximation by an appropriate diagonal matrix in quasi-Newton methods, with search directions in DL-type CG methods. The global convergence of the modified Dai-Liao conjugate gradient method has been proved on the set of uniformly convex functions. The efficiency and robustness of the newly presented methods are confirmed in comparison with similar methods, analyzing numerical results concerning the CPU time, a number of function evaluations, and the number of iterative steps. The proposed method is successfully applied to deal with an optimization problem arising in 2D robotic motion control.
Publisher: Hindawi

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