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Shor’s r-Algorithms: Theory and Practice

In: Optimization Methods and Applications

Author

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  • Petro I. Stetsyuk

    (V.M. Gluskov Institute of Cybernetics of NAS of Ukraine)

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.

Suggested Citation

  • Petro I. Stetsyuk, 2017. "Shor’s r-Algorithms: Theory and Practice," Springer Optimization and Its Applications, in: Sergiy Butenko & Panos M. Pardalos & Volodymyr Shylo (ed.), Optimization Methods and Applications, pages 495-520, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-68640-0_24
    DOI: 10.1007/978-3-319-68640-0_24
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