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.
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Notes
- 1.
As a matrix B 0 a diagonal matrix D n with positive coefficients on the diagonal is often chosen, with the help of which the variables are scaled.
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Acknowledgements
This work was supported by the National Academy of Sciences of Ukraine, project VF.120.19, and Volkswagen Foundation, grant No 90 306. The author would like to thank T.O. Bardadym, O.P. Lykhovyd, I.I. Parasyuk, and V.O. Zhydkov for their help in preparing this paper.
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Stetsyuk, P.I. (2017). Shor’s r-Algorithms: Theory and Practice. In: Butenko, S., Pardalos, P., Shylo, V. (eds) Optimization Methods and Applications . Springer Optimization and Its Applications, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-319-68640-0_24
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