Literature Cited
B. N. Pshenichnyi, “Convex multivalued mappings and their conjugates,” Kibernetika, No. 3, 94–102 (1972).
B. N. Pshenichnyi, “Necessary conditions of the extremum for differential inclusions,” Kibernetika, No. 6, 60–73 (1976).
V. V. Beresnev and B. N. Pshenichnyi, “On differential properties of minimum functions,” Zh. Vychisl. Mat. Mat. Fiz.,14, No. 3, 639–651 (1974).
V. V. Beresnev, “Mappings conjugate to convex multivalued mappings,” Kibernetika, No. 5, 79–83 (1973).
N. N. Dzyuba and B. N. Pshenichnyi, “On the discrete maximum principle,” Kibernetika, No. 2, 46–49 (1975).
B. N. Pshenichnyi and I. B. Medvedovskii, “A general result in convex analysis,” Kibernetika, No. 1, 60–63 (1976).
M. Sion, “On general minimax theorems,” Pacific J. Math.,8 (1958).
V. G. Boltyanskii, “The method of tents in the theory of extremal problems,” Usp. Mat. Nauk,30, No. 3, 3–56 (1975).
R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton (1970).
V. L. Makarov and A. M. Rubinov, A Mathematical Theory of Economic Dynamics and Equilibria [in Russian], Nauka, Moscow (1973).
A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems [in Russian], Nauka, Moscow (1974).
E. G. Gol'shtein, Theory of Duality in Mathematical Programming and Its Applications [in Russian], Nauka, Moscow (1971).
R. T. Rockafella, “Conjugate convex functions in optimal control and the calculus of variations,” J. Math. Anal. Appl.,32, No. 1, 174–222 (1970).
R. T. Rockafellar, “Existence and duality theorems for convex problems of Bolza,” Trans. Amer. Math. Soc.,159, No. 1, 1–40 (1971).
R. T. Rockafellar, “State constraints in convex problems of Bolza,” SIAM J. Control,10 No. 4, 691–715 (1972).
Additional information
Translated from Kibernetika, No. 3, pp. 105–111, May–June, 1977.
Rights and permissions
About this article
Cite this article
Pshenichyi, B.N., Medvedovskii, I.B. Duality in problems in the optimal control of processes described by convex multivalued mappings. Cybern Syst Anal 13, 423–429 (1977). https://doi.org/10.1007/BF01069663
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01069663