Suscripción a Biblioteca: Guest
Portal Digitalde Biblioteca Digital eLibros Revistas Referencias y Libros de Ponencias Colecciones
Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimir: 1064-2315
ISSN En Línea: 2163-9337

Volumen 51, 2019 Volumen 50, 2018 Volumen 49, 2017 Volumen 48, 2016 Volumen 47, 2015 Volumen 46, 2014 Volumen 45, 2013 Volumen 44, 2012 Volumen 43, 2011 Volumen 42, 2010 Volumen 41, 2009 Volumen 40, 2008 Volumen 39, 2007 Volumen 38, 2006 Volumen 37, 2005 Volumen 36, 2004 Volumen 35, 2003 Volumen 34, 2002 Volumen 33, 2001 Volumen 32, 2000 Volumen 31, 1999 Volumen 30, 1998 Volumen 29, 1997 Volumen 28, 1996

Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v44.i9.50
pages 51-65

General Scheme to Obtain Necessary Optimality Conditions for Continuous Optimal Set Partitioning Problems

Elena M. Kiseleva
Oles Honchar Dnipro National University, Dnepr
Alexandra A. Zhiltsova
Oles Honchar Dnepropetrovsk National University
Viktoriya A. Stroyeva
Dneprodzerzhynsk State Technical University


General continuous deterministic multiproduct optimal set partitioning problems are formulated in terms of the set function theory. The problems with constraints in the form of inequalities and those with constraints in the form of both equalities and inequalities are considered. For these problems, the necessary optimality conditions are obtained both in the general and constructive form, which can be easily applied to the specific classes of problems. The theorems application is illustrated by example of deterministic multiproduct nonlinear optimal set partitioning problem with the subset center arrangement and constraints in the form of equalities and inequalities.


  1. Kiseleva E.M., Shor N.Z. , Continuous problems of optimal set partitioning: theory, algorithms, applications [in Russian].

  2. Kiseleva E.M., Zhiltsova A.A. , The necessary optimality conditions for continuous problems of set partitioning in terms of the theory of set functions.

  3. Kiseleva E.M., Zhiltsova A.A. , Necessary optimality conditions in multiproduct OSP problem in terms of set function theory.

  4. Kiseleva E.M., Zhiltsova A.A. , Necessary and sufficient optimality conditions in problems of optimal set partitioning in terms of set functions. Dual problem.

  5. Kiseleva E.M., Stroyeva V.A. , Algorithm of solving of nonlinear continuous multicomponent problem of optimal set partitioning with placement of subsets centers.

  6. Kiseleva E.M., Zhiltsova A.A. , Some properties of partition space of continuous set.

  7. Lyapunov A.A. , On quite additive functions.

  8. Trukhaev P.N., Khomenyuk V.V. , Theory of nonclassical variational problems [in Russian].

  9. Kiseleva E.M., Hart L.L. , Elements of set functions theory [in Ukrainian].