Stetsyuk P.I.
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 rμ (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. © 2017, Springer Science+Business Media, LLC.

Keywords: adaptive step, conjugate gradient method, difference of subgradients, r-algorithm, software implementation, space dilation, steepest descent, subgradient method, Computation theory, Conjugate gradient method, Steepest descent method, adaptive step, difference of subgradients, Software implementation, space dilation, Sub-gradient methods, Iterative methods

Cite:
Stetsyuk P.I. (2017). Theory and software implementations of Shor's r-algorithms. Cybernetics and Systems Analysis, 53 (5), 43-57. doi: https://doi.org/10.1007/s10559-017-9971-1 http://jnas.nbuv.gov.ua/article/UJRN-0000754483 [In Russian].