Emets O. A.
On the Solution of Problems of Nonlinear Conditional Optimization on Arrangements by the Cut-Off Method
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.
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.
Optimization Problem on Permutations with Linear-Fractional Objective Function: Properties of the Set of Admissible Solutions
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.
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.
Extremal properties of nondifferentiable convex functions on euclidean sets of combinations with repetitions
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.