P. I. Stetsyuk

Algorithms of Nondifferentiable Optimization: Development and Application

A brief survey of nondifferentiable optimization methods developed at the Institute of Cybernetics is presented: the subgradient method, the subgradient method with space dilatation in the subgradient direction, and the r-algorithm. Applications of nondifferentiable optimization methods are considered.

An Approximate Method of Ellipsoids

AbstractA version of the method of ellipsoids is proposed in the paper that has the same asymptotic rate in volume convergence as the well-known Yudin-Nemirovskii-Shor method of ellipsoids. This method can be applied to one-dimensional problems, where it guarantees a decrease in the ratio of volumes equal to 2-

2d-Ellipsoid of optimal volume and its applications

\sqrt {{\text{Hz}}}

Models and information technologies for decision support during structural and technological changes

2 ≈ 0.5858 on each iteration.

Interindustry model of planned technological-structural changes

Nonsmooth-optimization methods with space expansion are considered as applied to decomposition schemes realized in solving two-stage problems of stochastic programming in the SLP—IOR simulation systems.

Problem Statements for k-Node Shortest Path and k-Node Shortest Cycle in a Complete Graph*

We consider space transformation operators for the outer approximation of the intersection of an ellipsoid and two half-spaces by an ellipsoid of smaller volume (2d-ellipsoid). We illustrate the connection between the space transformation and the anti-ravine technique in the Shors r-algorithms. The results of computational experiments are presented.

An approach to determining Shors dual quadratic estimates

The problems of finding the best one-dimensional and multidimensional linear models are considered for a short selection of measurement results with a rather small number of erroneous measurements. Using an example, it is shown that the least moduli method allows one to find models more adequate to the process than the least squares method.