Vasyl'yeva N. The optimality conditions and duality for the continuous optimal set partitioning problems

The object of research are continuous optimal partitionings of sets of n-dimensional euclidean space. The aim of research is to obtain theoretical statements for grounding and developing the methods and the algorithms of solving the continuous optimal set partitioning problems. The research has been conducted with using apparatus of extreme problems theory. The new differential and subdifferential optimality conditions like John and Kuhn-Tucker theorems have been built. The strong dual theorems in the presence of Lagrange functional saddle points have been proved. The existence of the original and dual problems solutions has been set up. Four estimates of the duality gap for the continuous optimal set partitioning problems have been got. The spheres of use are economics (planning), technique (design, signal classification).