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A Hybrid Conjugate Gradient Algorithm Using the Golden Section Ratio for Unconstrained Optimization Problems | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Articles in Press, Corrected Proof, Available Online from 05 August 2025 | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2025.159795.1187 | ||
| Authors | ||
| Sara Sahib Mohammed Zaki* 1; Hawraz Nadhim Jabbar2; Sozan Saber Haider3 | ||
| 1University of Sulaimani-College of Science | ||
| 2University of Kirkuk-College of Science | ||
| 3University of Sulaimani-College of Administration and Economics | ||
| Abstract | ||
| Conjugate gradient techniques are highly effective for addressing large-scale nonlinear optimization problems. Hybridization is a prevalent strategy for improving the conjugate gradient method. This study presents a novel hybrid conjugate gradient (CG) algorithm that incorporates the golden section ratio for solving unconstrained optimization problems. Hence, we improve the efficiency and robustness of traditional CG methods by taking advantage of the properties of the golden section ratio, which is known for its optimality in line search procedures. Therefore, this study explores the novel use of the golden section ratios (0.382) and (0.618) as a weighting factor (β) in a hybrid convex combination under Dai-Liao condition of two pairs of standard conjugate gradient methods: (β^HS, β^DY) and (β^LS, β^CD) separately. These formulas are fundamental to conjugate gradient methods and provide clear benefits in optimization situations. The suggested strategies seek to capitalize on the advantages of the approaches while minimizing their drawbacks by including the golden section ratio which is known for reducing computational cost, improving step size selection, and ensuring robust convergence especially in ill-conditioned problems in optimization. The numerical results show how effective the suggested approaches are. | ||
| Keywords | ||
| Unconstrained Optimization; Hybrid Conjugate Gradient; the Golden section ratios; Convex Combination; Sufficient Descent Condition | ||
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