Improved Dai–Liao Conjugate Gradient Methods for Large-Scale Unconstrained Optimization

Hassan, Basim A.; Ibrahim, Alaa Luqman; Mehamdia, Abd Elhamid

doi:10.33899/csmj.2025.159774.1186

	Improved Dai–Liao Conjugate Gradient Methods for Large-Scale Unconstrained Optimization
AL-Rafidain Journal of Computer Sciences and Mathematics
Article 19, Volume 19, Issue 1, June 2025, Pages 178-186 PDF (700.06 K)
Document Type: Research Paper
DOI: 10.33899/csmj.2025.159774.1186
Authors
Basim A. Hassan^* ¹; Alaa Luqman Ibrahim²; abd elhamid mehamdia³
¹Department of Mathematics, College of Computers Sciences and Mathematics University of Mosul, Mosul, Iraq
²Department of Mathematics, College of Science, University of Zakho, Zakho, Kurdistan Region, Iraq
³Universite M'hamed Bougara, boumerdes
Abstract
This research introduces and evaluates two enhanced conjugate gradient methods for unconstrained optimization, building upon the Dai–Liao conjugacy condition and further refined through the application of Taylor series expansion. These novel methodologies were rigorously compared against the classical Hestenes-Stiefel (HS) method using a diverse suite of benchmark test functions. The numerical results obtained unequivocally demonstrate a significant improvement in computational efficiency achieved by the proposed methods. Notably, our enhanced methods consistently outperformed the HS method across several critical performance metrics, including a reduction in the number of iterations required for convergence, a decrease in the total number of function evaluations, and an overall faster computation time
Keywords
Unconstrained Optimization; Secant Condition; Conjugate Gradient Method; Dai–Liao Method; Computational Efficiency

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