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Journal of Automation and Information Sciences
SJR: 0.238 SNIP: 0.464 CiteScore™: 0.27

ISSN Print: 1064-2315
ISSN Online: 2163-9337

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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].

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