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On the Solution of a Locally Finite System of Linear Inequalities with Graph Structure

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Ukrainian Mathematical Journal Aims and scope

Abstract

We propose a method for the solution of a locally finite system of linear inequalities that arises in the course of solution of problems of control over resource in networks with generalized Kirchhoff law. We present a criterion for a system of inequalities to have the graph structure.

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REFERENCES

  1. V. V. Ostapenko and A. I. Pavlygin, “Linear inequalities for the generalized Kirchhoff law,” Kibern. Syst. Analiz, No. 3, 130–148 (1997).

  2. V. V. Ostapenko, A. I. Pavlygin, and G. S. Finin, “A generalized principle of conservation of flows in networks,” in: Proceedings of the Third Conference on Automatic Control “Avtomatika-96” (Sevastopol, 1996) [in Russian], Vol. 2, Sevastopol Technical Institute, Sevastopol (1996), p. 137.

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  3. G. S. Finin, “On the solution of systems of linear inequalities by methods of elimination of unknowns,” Vestn. Mezhd. Solomon Univ., No. 1, 116–122 (1999).

  4. V. V. Ostapenko and A. I. Pavlygin, “Dynamic flows in networks for the generalized Kirchhoff law,” Kibern. Syst. Analiz, No. 3, 96–102 (1996).

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Authors and Affiliations

  1. Institute of Applied Systems Analysis, Ukrainian Ministry of Education, Ukrainian Academy of Sciences Kiev, Ukraine

    V. V. Ostapenko

  2. International Solomon University, Ukraine

    G. S. Finin

Authors
  1. V. V. Ostapenko
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  2. G. S. Finin
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Ostapenko, V.V., Finin, G.S. On the Solution of a Locally Finite System of Linear Inequalities with Graph Structure. Ukrainian Mathematical Journal 53, 652–655 (2001). https://doi.org/10.1023/A:1012391024533

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  • DOI: https://doi.org/10.1023/A:1012391024533

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