On solutions properties of continuous linear problems of optimal multiplex-partitioning of sets without constraints

Abstract

The paper presents some properties of the solutions of continuous problems of optimal multiplex-partitioning of sets. Such problems are considered in two versions: with given coordinates of centers or with their placing in a given region. The optimal solutions of continuous linear problems of optimal multiplex-partitioning of sets is obtained analytically as characteristic vector-functions of the k-th order subsets included into the optimal multiplex partition of the set Ω.