Theory and Software Implementations of Shor’s r-Algorithms

Three computational forms of r -algorithms with different amount of computation per iteration are considered. The results on the convergence of the limit variant of r -algorithms for convex smooth functions and the r μ ( α )-algorithm for convex piecewise smooth functions are presented. Practical as...

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Bibliographic Details
Published in:Cybernetics and systems analysis 2017-09, Vol.53 (5), p.692-703
Main Author: Stetsyuk, P. I.
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Control
Mathematics
Mathematics and Statistics
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Analysis
Systems Theory
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Summary:Three computational forms of r -algorithms with different amount of computation per iteration are considered. The results on the convergence of the limit variant of r -algorithms for convex smooth functions and the r μ ( α )-algorithm for convex piecewise smooth functions are presented. Practical aspects of the variant of r ( α )-algorithms with a constant coefficient of space dilation α and an adaptive method for step adjustment in the direction of the normalized anti-subgradient in the transformed space of variables are discussed.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-017-9971-1