Scaling on the Spectral Gradient Method

This paper presents a new method for steplength selection in the frame of spectral gradient methods. The steplength formula is based on the interpolation scheme as well as some modified secant equations. The corresponding algorithm selects the initial positive steplength per iteration according to t...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2013-08, Vol.158 (2), p.626-635
Main Authors: Biglari, Fahimeh, Solimanpur, Maghsud
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applications of Mathematics
Approximation
Calculus of Variations and Optimal Control
Optimization
Engineering
Frames
Interpolation
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Nonlinear equations
Operations Research/Decision Theory
Optimization
Spectra
Studies
Theory of Computation
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Summary:This paper presents a new method for steplength selection in the frame of spectral gradient methods. The steplength formula is based on the interpolation scheme as well as some modified secant equations. The corresponding algorithm selects the initial positive steplength per iteration according to the satisfaction of the secant condition, and then a backtracking procedure along the negative gradient is performed. The numerical experience shows that this algorithm improves favorably the efficiency property of the standard Barzilai–Borwein method as well as some other recently modified Barzilai–Borwein approaches.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0265-5