This is a preview of subscription content, log in via an institution to check access.
Literature Cited
A. Ya. Dubovitskii and A. A. Milyutin, “Extremum problems in the presence of constraints,” Zh. Vychisl. Mat. Mat. Fiz.,5, No. 3, 395–453 (1965).
A. A. Milyutin, “General schemes for obtaining necessary conditions of extremum in optimal control problems,” Usp. Mat. Nauk,25, No. 5, 110–116 (1970).
A. Ya. Dubovitskii and A. A. Milyutin, Necessary Conditions of Weak Extremum in the General Problem of Optimal Control [in Russian], Nauka, Moscow (1971).
V. G. Boltyanskii, “The method of tents in the theory of experimental problems,” Usp. Mat. Nauk,30, 3–35 (1975).
L. W. Neustadt, “An abstract variational theory with application to a broad class of optimization problems. I. General theory,” SIAM J. Control,4, No. 3, 505–527 (1966).
R. V. Gamkrelidze and G. L. Karatashvili, “Extremal problems in linear topological spaces,” Izv. Akad. Nauk SSSR, Ser. Mat.,33, No. 4, 781–839 (1969).
L. A. Lyusternik, “On the conditional extremum of functionals,” Mat. Sb.,41, No. 3, 390–401 (1934).
L. A. Lyusternik and V. I. Sobolev, Elements of Functional Analysis [in Russian], Nauka, Moscow (1965).
V. A. Balabanov, “On the conditional minimum of a functional in topological vector spaces,” Tr. Tbil. Mat. Inst. Akad. Nauk. Gruz. SSR,36, 5–28 (1970).
M. M. Vainberg and L. Ya. Éngel'son, “On the conditional extremum of functionals in linear topological spaces,” Mat. Sb.,45, No. 5, 417–422 (1958).
B. N. Pshenichnyi, Necessary Conditions for Extremum [in Russian], Nauka, Moscow (1969).
S. Kurcyusz, “On the existence of Lagrange multipliers for infinite dimensional extremum problems,” Bull. Acad. Polon. Sci. Techn.,22, No. 9, 799–802 (1974).
K. Sh. Tsiskaridze, “Extremal problems in Banach spaces,” in: Problems in the Mathematical Theory of Optimal Control, Vol. I, Izd. Tbil. Univ., (1975), pp. 5–150.
M. V. Sukhinin, “On the conditional extremum of functionals in linear topological spaces,” Mat. Zametki,14, No. 3, 375–382 (1973).
M. V. Sukhinin, “Two theorems on the conditional minimum of functionals in locally convex spaces,” Usp. Mat. Nauk,30, No. 3, 175–176 (1975).
Fan Ky, “Fixed point and minimax theorems in locally convex topological linear spaces,” Proc. Nat. Acad. Sci. USA,38, 121–126 (1952).
R. E. Edwards, Functional Analysis. Theory and Applications, Holt, Reinhart and Winston, New York (1965).
L. V. Katorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).
A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems [in Russian], Nauka, Moscow (1974).
A. V. Dmitruk, “On the foundation of the method of sliding regimes for optimal control problems with mixed constraints,” Funkts. Anal. Prilozhen.,10, No. 3, 39–44 (1976).
V. I. Averbukh and O. G. Smolyanov, “Various definitions of the derivative in linear topological spaces,” Usp. Mat. Nauk,23, No. 4, 67–116 (1968).
M. F. Sukhinin, “The rule of Lagrange multipliers as a necessary and sufficient condition for quasicriticality of maps of Banach spaces,” Usp. Mat. Nauk,33, No. 2, 183–184 (1978).
H. Schaefer, Topological Vector Spaces, MacMillan, New York (1966).
M. M. Fel'dman, “On sufficient conditions for the existence of supports to sublinear operators,” Sib. Mat. Zh.,16, No. 1, 132–138 (1975).
M. A. Krasnosel'skii, P. P. Zabreiko, E. I. Pustyl'nik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions [in Russian], Nauka, Moscow (1966).
M. A. Krasnosel'skii and P. P. Zabreiko, Geometrical Methods of the Nonlinear Analysis [in Russian], Nauka, Moscow (1975).
Additional information
Moscow Textile Institute. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 23, No. 4, pp. 153–165, July–August, 1982.
Rights and permissions
About this article
Cite this article
Sukhinin, M.F. The rule of Lagrange multipliers in locally convex spaces. Sib Math J 23, 569–579 (1982). https://doi.org/10.1007/BF00968662
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00968662