Skip to main content
Log in

Dynamic Programming in the Problem of Decomposition Optimization

  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Consideration was given to the “operator” version of the dynamic programming method in the problem of decomposing a nonempty set in the presence of inexact calculations of the Bellman function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. Minoux, M., Programmation mathématique. Théorie et algorithmes, Paris: Dunod, 1983. Translated under the title Matematicheskoe programmirovanie, Moscow: Nauka, 1990.

    Google Scholar 

  2. Bellman, R., Applying Dynamic Programming to the Travelling Salesman Problem, Kibern. Sb., 1964, vol. 9.

  3. Kheld, M. and Karp, R.M., Applying Dynamic Programming to the Ordering Problems, Kibern. Sb., 1964, vol. 9.

  4. Korotaeva, L.N., Sesekin, A.N., and Chentsov, A.G., On a Modification of the Dynamic Programming Method in the Problem of Successive Approach, Zh. Vychisl. Mat. Mat. Fiz., 1989, vol. 29, no. 8, pp. 1107–1113.

    Google Scholar 

  5. Korotaeva, L.N., Nazarov, E.M., and Chentsov, A.G., On an Assignment Problem, Zh. Vychisl. Mat. Mat. Fiz., 1993, vol. 33, no. 4, pp. 483–494.

    Google Scholar 

  6. Korotaeva, L.N. and Chentsov, A.G., On a Generalization of the Travelling Salesman Problem to “Bottlenecks,” Zh. Vychisl. Mat. Mat. Fiz., 1995, vol. 35, no. 7, pp. 1067–1076.

    Google Scholar 

  7. Chentsov, A.G. and Korotayeva, L.N., The Dynamic Programming Method in the Generalized Salesman Problem, Math. Comput. Modeling, 1997, vol. 25, no. 1, pp. 93–105.

    Google Scholar 

  8. Korotaeva, L.N., Trukhin, M.P., and Chentsov, A.G., On Routing of Connections, Avtom. Telemekh., 1997, no. 12, pp. 175–192.

  9. Zobnin, B.B., Korotaeva, L.N., and Chentsov, A.G., On a Problem Route Optimization and Its Applications, Probl. Peredachi Inf., 1997, vol. 33, no. 4, pp. 1–18.

    Google Scholar 

  10. Chentsov, A.A. and Chentsov, A.G., On Solution of the Problem of Route Optimization by the Dynamic Programming Method, Avtom. Telemekh., 1998, no. 9, pp. 117–129.

  11. Sabiryanova, K.G. and Chentsov, A.G., Dynamic Programming in the Problem of Covering Optimization, Avtom. Telemekh., 1994, no. 3, pp. 54–64.

  12. Chentsov, A.G. and Chentsov, P.A., On Constructing the Decomposition Procedure of a Finite Set by the Dynamic Programming Method, Avtom. Telemekh., 2000, no. 4, pp. 129–142.

  13. Neveu, J., Bases mathée matiques du calcul des probabilités, Paris: Masson & Cie, 1964. Translated under the title Matematicheskie osnovy teorii veroyatnostei, Moscow: Mir, 1969.

    Google Scholar 

  14. Dunford, N. and Schwartz, J.T., Linear Operators, New York: Interscience, 1958. Translated under the title Lineinye operatory. Obshchaya teoriya, Moscow: Inostrannaya Litetatura, 1962.

    Google Scholar 

  15. Dieudonné, J., Foundations of Modern Analysis, New York, Academic, 1960. Translated under the title Osnovy sovremennogo analiza, Moscow: Mir, 1964.

    Google Scholar 

  16. Chentsov, A.A. and Chentsov, A.G., Dynamic Programming Method in the Generalized Traveling Salesman Problem: The Influence of Inexact Calculations, Math. Comput. Modeling, 2001, vol. 33, pp. 801–819.

    Google Scholar 

  17. Engelking, R., General Topology, Warszawa: PWN, 1985. Translated under the title Obshchaya topologiya, Moscow: Mir, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chentsov, A.G., Chentsov, P.A. Dynamic Programming in the Problem of Decomposition Optimization. Automation and Remote Control 63, 815–828 (2002). https://doi.org/10.1023/A:1015406222958

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015406222958

Keywords

Navigation