Two classes of spectral conjugate gradient methods for unconstrained optimizations

The spectral conjugate gradient method is effective iteration method for solving large-scale unconstrained optimizations. In this paper, using the strong Wolfe line search to yield the spectral parameter, and giving two approaches to choose the conjugate parameter, then two classes of spectral conju...

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Published inJournal of applied mathematics & computing Vol. 68; no. 6; pp. 4435 - 4456
Main Authors Jian, Jinbao, Liu, Pengjie, Jiang, Xianzhen, Zhang, Chen
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2022
Springer Nature B.V
Subjects
Applied mathematics
Computational Mathematics and Numerical Analysis
Conjugate gradient method
Iterative methods
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical methods
Original Research
Parameters
Theory of Computation
Global convergence
Unconstrained optimization
90C30
90C25
Strong Wolfe line search
Spectral conjugate gradient method
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Summary:The spectral conjugate gradient method is effective iteration method for solving large-scale unconstrained optimizations. In this paper, using the strong Wolfe line search to yield the spectral parameter, and giving two approaches to choose the conjugate parameter, then two classes of spectral conjugate gradient methods are established. Under usual assumptions, the proposed methods are proved to possess sufficient descent property and global convergence. Taking some specific existing conjugate parameters to test the validity of the two classes of methods, and choosing the best method from each class to compare with other efficient conjugate gradient methods, respectively. Large-scale numerical results for the experiments are reported, which show that the proposed methods are promising.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-022-01713-2