Literature Cited
V. F. Dem'yanov, Minimax: Differentiability along Directions [in Russian], Leningrad State Univ. (1974).
E. G. Gol'shtein, Convex Programming. Elements of the Theory [in Russian], Nauka, Moscow (1970).
O. F. Borisenko and L. I. Minchenko, “On directional differentiability of the maximum function,” Zh. Vychisl. Mat. Mat. Fiz.,23, No. 3, 567–575 (1983).
A. I. Sotskov, “Necessary conditions for maximum under connected constraints,” Kibernetika, No. 4, 96–102 (1970).
Yu. I. Tyurin, “Mathematical formulation of a simplified model of production planning,” Ekonomika Mat. Met.,1, No. 3, 391–410 (1965).
B. N. Pshenichnyi, Convex Analysis and Extremal Problems [in Russian], Nauka, Moscow (1980).
W. W. Hogan, “Directional derivatives for extremal value functions with applications to the completely completely convex case,” Oper. Res.,21, 188–209 (1973).
N. A. Pecherskaya, “On conditions for directional differentiability of the maximum function under connected constraints,” in: Operation Research (Models, Systems, Solutions) [in Russian], No. 5, VTs. Akad. Nauk SSSR, Moscow (1976), pp. 11–16.
N. A. Pecherskaya, “Differentiability of multivalued maps,” in: Nonsmooth Problems of Optimization and Control Theory [in Russian], Leningrad State Univ. (1982), pp. 128–147.
V. L. Makarov and A. M. Rubinov, Mathematical Theory of Economic Dynamics and Equilibrium [in Russian], Nauka, Moscow (1973).
J. P. Aubin, “Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions,” Math. Anal. Appl.,7a 159–229 (1981).
Yu. G. Borisovich, B. L. Gel'man, A. D. Myshkis, and V. V. Obukhovskii, “Multivalued mappings,” J. Sov. Math.,24, No. 6 (1984).
V. F. Dem'yanov and A. M. Rubinov, “Elements of quasidifferential calculus,” in: Nonsmooth problems of Optimization and Control Theory [in Russian], Leningrad State Univ. (1982), pp. 5–127.
V. F. Dem'yanov and A. M. Rubinov, Approximate Methods for Solving Extremal Problems [in Russian], Leningrad State Univ. (1968).
R. T. Rockafellar, “Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming,” Math. Program. Studies,17, 28–66 (1982).
A. M. Rubinov, Superlinear Multivalued Maps and Their Applications to Economic-Mathematical Models [in Russian], Nauka, Leningrad (1980).
B. N. Pshenichnyi, Necessary Conditions of Extremum [in Russian], Nauka, Moscow (1982).
Additional information
Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 26, No. 3, pp. 147–155, May–June, 1985.
Rights and permissions
About this article
Cite this article
Rubinov, A.M. Conjugate derivative of a multivalued mapping and the differentiability of the maximum under connectedconstraints. Sib Math J 26, 424–431 (1985). https://doi.org/10.1007/BF00968631
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00968631