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.
Similar content being viewed by others
REFERENCES
Minoux, M., Programmation mathématique. Théorie et algorithmes, Paris: Dunod, 1983. Translated under the title Matematicheskoe programmirovanie, Moscow: Nauka, 1990.
Bellman, R., Applying Dynamic Programming to the Travelling Salesman Problem, Kibern. Sb., 1964, vol. 9.
Kheld, M. and Karp, R.M., Applying Dynamic Programming to the Ordering Problems, Kibern. Sb., 1964, vol. 9.
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.
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.
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.
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.
Korotaeva, L.N., Trukhin, M.P., and Chentsov, A.G., On Routing of Connections, Avtom. Telemekh., 1997, no. 12, pp. 175–192.
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.
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.
Sabiryanova, K.G. and Chentsov, A.G., Dynamic Programming in the Problem of Covering Optimization, Avtom. Telemekh., 1994, no. 3, pp. 54–64.
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.
Neveu, J., Bases mathée matiques du calcul des probabilités, Paris: Masson & Cie, 1964. Translated under the title Matematicheskie osnovy teorii veroyatnostei, Moscow: Mir, 1969.
Dunford, N. and Schwartz, J.T., Linear Operators, New York: Interscience, 1958. Translated under the title Lineinye operatory. Obshchaya teoriya, Moscow: Inostrannaya Litetatura, 1962.
Dieudonné, J., Foundations of Modern Analysis, New York, Academic, 1960. Translated under the title Osnovy sovremennogo analiza, Moscow: Mir, 1964.
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.
Engelking, R., General Topology, Warszawa: PWN, 1985. Translated under the title Obshchaya topologiya, Moscow: Mir, 1986.
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1023/A:1015406222958