Abstract
Two improved nonlinear conjugate gradient methods are proposed by using the second inequality of the strong Wolfe line search. Under usual assumptions, we proved that the improved methods possess the sufficient descent property and global convergence. By testing the unconstrained optimization problems which taken from the CUTE library and other usual test collections, some large-scale numerical experiments for the presented methods and their comparisons are executed. The detailed results are listed in tables and their corresponding performance profiles are reported in figures, which show that our improved methods are superior to their comparisons.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (11771383), the Natural Science Foundation of Guangxi Province (2020GXNSFDA238017, 2018GXNSFFA281007) and Research Project of Guangxi University for Nationalities (2018KJQ-D02).
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All authors read and approved the final manuscript. JJ mainly contributed to the algorithm design; PL and XJ mainly contributed to the convergence analysis, numerical results and drafted the manuscript; BH mainly contributed to the convergence analysis.
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Communicated by Rohollah Yousefpour.
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Jian, J., Liu, P., Jiang, X. et al. Two Improved Nonlinear Conjugate Gradient Methods with the Strong Wolfe Line Search. Bull. Iran. Math. Soc. 48, 2297–2319 (2022). https://doi.org/10.1007/s41980-021-00647-y
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DOI: https://doi.org/10.1007/s41980-021-00647-y
Keywords
- Unconstrained optimization
- Conjugate gradient method
- Strong Wolfe line search
- Sufficient descent property
- Global convergence