1. Home
  2. LEA 2015
  3. Proceedings
  4. On solutions properties of continuous linear problems of optimal multiplex-partitioning of sets without constraints

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

Antonina Cherevatenko1 pavlova-tonya [at] mail.ru
  1. Computational Mathematics and Mathematical Cybernetics Department, Oles Honchar Dnipropetrovsk National University, Ukraine, Dnepropetrovsk, Karl Marx Ave., 35
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 

Keywords 
sets partitioning of the k-th order
optimal multiplex-partitioning of set
continuous problems of optimal sets partitioning
Voronoi diagrams of the k -th order
References 

[1] L. S. Koriashkina, "Extension of one class of infinitedimensional optimization problems", Cherkasy University Bulletin: Scientific journal. Applied mathematics. Informatics (in Ukrainian), vol. 18 (351), 2015, pp. 28 – 36.
[2] E. M. Kiseleva, L. S. Koriashkina, "Models and Methods for Solving Continuous Problems of Optimal Set Partitioning: Linear, Nonlinear, and Dynamic Problems" (in Russian), Naukova Dumka, 2013, 606 pp.
[3] F. P. Preparata, M. I. Shamos, "Computational Geometry: An Introduction (Texts and Monographs in Computer Science)", Springer-Verlag New York, 1985, 390 pp.
[4] E. M. Kiseleva, L. S. Koriashkina, "Theory of Continuous Optimal Set Partitioning Problems as a Universal Mathematical Formalism for Constructing Voronoi Diagrams and Their Generalizations. I. Theoretical Foundations", Cybernetics and Systems Analysis, Vol. 3 (51), May 2015, pp. 325 – 335.
[5] E. M. Kiseleva, L. S. Koriashkina, "The Theory of Continuous Optimal Set Partitioning Problems as a Universal Mathematical Formalism for Constructing the Voronoi Diagram and its Generalizations. II. Algorithms for constructing Voronoi Diagrams based on the theory of optimal partitioning of sets", Cybernetics and Systems Analysis, Vol. 4 (51), May 2015, pp. 489 – 499.