2019
Том 71
№ 9

All Issues

Emets O. A.

Articles: 5
Article (Ukrainian)

On the Solution of Problems of Nonlinear Conditional Optimization on Arrangements by the Cut-Off Method

Barbolina T. M., Emets O. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 604-611

We propose an exact method for the solution of a minimization problem on arrangements of a linear objective function with linear and concave additional constraints. We prove the finiteness of the proposed algorithm of the cut-off method.

Article (Ukrainian)

Irreducible System of Constraints for a General Polyhedron of Arrangements

Emets O. A., Nedobachii S. I., Roskladka О. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 3-11

We construct a system of constraints for a general polyhedron of arrangements that does not contain superfluous inequalities. The derivation of an irreducible system enables one to substantially reduce the number of operations necessary for finding exact solutions of optimization problems on arrangements.

Article (Ukrainian)

Optimization Problem on Permutations with Linear-Fractional Objective Function: Properties of the Set of Admissible Solutions

Emets O. A., Kolechkina L. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 12. - pp. 1630-1640

We consider an optimization problem on permutations with a linear-fractional objective function. We investigate the properties of the domain of admissible solutions of the problem.

Brief Communications (Ukrainian)

On estimates of minima of criterion functions in optimization on combinations

Emets O. A., Roskladka О. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 8. - pp. 1118–1121

On the basis of the approach proposed, we obtain new estimates of extremal values of strongly convex differentiable functions and strengthened estimates of minima on a set of combinations with repetions.

Article (Russian)

Extremal properties of nondifferentiable convex functions on euclidean sets of combinations with repetitions

Emets O. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 680–691

A general approach is suggested for studying extremal properties of nondifferentiable convex functions on Euclidean combinatorial sets. On the basis of this approach, by solving the linear optimization problem on a set of combinations with repetitions, we obtain estimates of minimum values of convex and strongly convex objective functions in optimization problems on sets of combinations with repetitions and establish sufficient conditions for the existence of the corresponding minima.