Article information

2017 , Volume 22, 2, p.127-149

Stetsyuk P.I.

Subgradient methods ralgb5 and ralgb4 for minimization of ravine-like convex functions

We consider properties of the three computational forms of the 𝑟-algorithm proposed by N.Z. Shor for optimization of non-smooth functions that differ in the complexity of a single iteration. Discussed is a variant of the 𝑟-algorithm with adaptive stepsize control along the direction of the normalized antisubgradient in the transformed space of variables. The Octave functions ralgb5 and ralgb4 are described, which implement two computationally stable forms of the 𝑟-algorithms with adaptive stepsize control and a constant space dilation factor. The results of computational experiments for an essentially ravine-like piecewise quadratic function and a piecewise linear function related to solvability of interval linear tolerance problem are presented.

[full text]
Keywords: subgradient method, space dilation, r-algorithm, adaptive stepsize control, GNU Octave, Octave function, piecewise-quadratic function maxquad, interval linear tolerance problem

Author(s):
Stetsyuk Petr Ivanovich
Dr.
Position: Head of Departament
Office: V.M.Glushkov Institute of cybernetics of National Academy of Sciences of Ukraine
Address: 03680, Ukraine, Kiev, 40, acad. Glushkov avenue
Phone Office: (044) 526-21-68
E-mail: stetsyukp@gmail.com

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Bibliography link:
Stetsyuk P.I. Subgradient methods ralgb5 and ralgb4 for minimization of ravine-like convex functions // Computational technologies. 2017. V. 22. 2. P. 127-149
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