Automation and Remote Control

, Volume 79, Issue 9, pp 1703–1712 | Cite as

Mathematical Programming Problems Solving by Functional Voxel Method

  • A. V. TolokEmail author
  • N. B. Tolok
Control Sciences


One of the approaches to mathematical programming problems solving by means of R-functional modeling is considered. Some functional voxel method tools are presented for the wide class of optimization problems computer solution using voxel algorithm of gradient descent. The illustrative examples of the computer calculations in comparison to non-computer solutions are given.


R-function R-functional modeling voxel local geometrical characteristics the functional voxel method functional voxel model M-image mathematical programming 


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  1. 1.
    Maksimenko-Sheiko, K.V., R-functions in Mathematical Modeling of Geometric Objects and Physical Fields, Kharkov: IPMash, 2009.zbMATHGoogle Scholar
  2. 2.
    Rvachev, V.L., Teoriya R-funktsii i nekotorye ee prilozheniya (Theory of R-Functions and Some Its Applications), Kiev: Naukova Dumka, 1982.zbMATHGoogle Scholar
  3. 3.
    Tolok, A.V., Funktsional’no-voksel’nyi metod v komp’yuternom modelirovanii (Functional Voxel Method in Computer Modeling), Moscow: Fizmatlit, 2016.Google Scholar
  4. 4.
    Vasilyev, S.N., Loktev, M.A., Tolok, A.V., Tolok, N.B., and Ulyanov, S.A., Route Planning in 3D Environment with a Multivariant Model, Tr. SPIIRAN, 2016, vol. 45, no. 2, pp. 5–25.Google Scholar
  5. 5.
    Grigoriev, S.N., Loktev, M.A., and Tolok, A.V., Construction of Voxel Models of Geometric Objects, Prikl. Informat., 2013, vol. 46, no. 4, pp. 50–55.Google Scholar
  6. 6.
    Grigoriev, S.N., Lotorevich, E.A., Pushkarev, S.A., Silantiev, D.A., and Tolok, A.,V., Automating Graphic Techniques for Solving Some Mathematical Problems, Prikl. Informat., 2012, vol. 41, no. 5, pp. 44–50.Google Scholar
  7. 7.
    Kovalev, S.P. and Tolok, A.V., Model-based Approach to Lifecycle Management of Complex Technical Products, Inform. Tekhnol. Proekt. Proizv., 2015, vol. 158, no. 2, pp. 3–9.Google Scholar
  8. 8.
    Silantyev, D.A., Lotorevich, E.A., Pushkaryov, S.A., and Tolok, A.V., Voxel-Mathematical Modelling at the Solution of Problems of Definition of Working Surfaces Of Details, Inform. Tekhnol. Proekt. Proizv., 2013, no. 3, pp. 29–33.Google Scholar
  9. 9.
    Barskii, A.B., Parallel’nye informatsionnye tekhnologii (Parallel Information Technologies), Moscow: BINOM, 2007.Google Scholar
  10. 10.
    Monakhov, V.M., Metody optimizatsii. Primenenie matematicheskikh metodov v ekonomike (Methods of Optimization. Application of Mathematical Methods in Economics), Moscow: Prosveshchenie, 1978.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

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