Shor’s r-Algorithms: Theory and Practice

Petro I. Stetsyuk ()
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Petro I. Stetsyuk: V.M. Gluskov Institute of Cybernetics of NAS of Ukraine

A chapter in Optimization Methods and Applications, 2017, pp 495-520 from Springer

Abstract: Abstract Properties of three computational forms of r-algorithms differentiated by their complexities (number of calculations per iteration) are considered. The results on convergence of the limit variants of r-algorithms for smooth functions and r μ (α)-algorithm for nondifferentiable functions are presented. A variant of r(α)-algorithms with a constant coefficient of space dilation α and adaptive step adjustment along the normalized anti-subgradient in the transformed space of variables is discussed. Octave-functions ralgb5 and ralgb4 of r(α)-algorithms with adaptive step adjustment are described. The results of computational experiments for substantially ravine piecewise quadratic function and ravine quadratic and piecewise linear functions are presented.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-68640-0_24

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DOI: 10.1007/978-3-319-68640-0_24

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