Ostapenko V. V.
Ukr. Mat. Zh. - 2001. - 53, № 4. - pp. 568-571
We propose a method for the solution of a locally finite system of linear inequalities that arises in the course of solution of problems of control over resource in networks with generalized Kirchhoff law. We present a criterion for a system of inequalities to have the graph structure.
Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 50-56
We study methods for the elimination of an unknown or a group of unknowns from systems of linear inequalities. We justify these methods by using the Helly theorem. The methods considered are applied to the calculation of streams in networks with a generalized conservation law.
Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 64–69
The notion of a convex set is generalized. In the definition of ordinary convexity, sums of products of vectors and numbers are used. In the generalization considered in this paper, the role of numbers is played by matrices; this is why we call it “matrix convexity.”
Ukr. Mat. Zh. - 1987. - 39, № 5. - pp. 588–592
Ukr. Mat. Zh. - 1983. - 35, № 2. - pp. 169—172
Ukr. Mat. Zh. - 1980. - 32, № 2. - pp. 175 - 178
Ukr. Mat. Zh. - 1978. - 30, № 3. - pp. 400– 403