Abstract. We consider a mathematical model of the dynamic problem of partitioning a set from Rⁿ with the arrangement of centers of subsets under joint constraints on the partition and phase variable. We describe a solution method that synthesizes the basic provisions of the theory of continuous partitioning problems and optimal control theory of dynamic systems. We present a numerical solution algorithm and analyze the results of computational experiments.

Keywords: continuous problem of optimal set partitioning, controlled system, Lagrange functional, nondifferentiable optimization method.