The new spectral conjugate gradient method for large-scale unconstrained optimisation

The spectral conjugate gradient methods are very interesting and have been proved to be effective for strictly convex quadratic minimisation. In this paper, a new spectral conjugate gradient method is proposed to solve large-scale unconstrained optimisation problems. Motivated by the advantages of a...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2020; no. 1; pp. 1 - 11
Main Authors Wang, Li, Cao, Mingyuan, Xing, Funa, Yang, Yueting
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 25.04.2020
Springer Nature B.V
SpringerOpen
Subjects
Algorithms
Analysis
Applications of Mathematics
Approximate optimal stepsize
Approximation
Conjugate gradient method
Conjugates
Global convergence
Mathematics
Mathematics and Statistics
Methods
Optimization
Spectra
Spectral conjugate gradient method
Approximate optimal stepsize
Global convergence
Spectral conjugate gradient method
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Summary:The spectral conjugate gradient methods are very interesting and have been proved to be effective for strictly convex quadratic minimisation. In this paper, a new spectral conjugate gradient method is proposed to solve large-scale unconstrained optimisation problems. Motivated by the advantages of approximate optimal stepsize strategy used in the gradient method, we design a new scheme for the choices of the spectral and conjugate parameters. Furthermore, the new search direction satisfies the spectral property and sufficient descent condition. Under some suitable assumptions, the global convergence of the developed method is established. Numerical comparisons show better behaviour of the proposed method with respect to some existing methods for a set of 130 test problems.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02375-z