Literature Cited
A. Ya. Dubovitskii and A. A. Milyutin, “Extremum problems in the presence of constraints,” Zh. Vychisl. Matem. i Matem. Fiz.,5, No. 3 (1965).
H. Halkin and L.W. Neustadt, “General necessary conditions for optimization problems,” Proc. Nat. Acad. Sciences U. S.,56, 1066–1071 (1966).
H. Halkin, Nonlinear Nonconvex Programming in an Infinite Dimensional Space, Mathematical Theory of Control, Academic Press (1967).
B.N. Pshenichnyi, Necessary Conditions for an Extremum [in Russian], Nauka, Moscow (1969).
K.J. Arrow and L. Hurwicz, Studies in Linear Programming [Russian translation], IL, Moscow (1962).
L.W. Neustadt, “A general theory of extremals,” J. Comput. System Sci.,3, No. 1, 57–92 (1969).
Y. Nagahisa and Y. Sakawa, “Nonlinear programming in Banach spaces,” J. Optimization Theory Appl.,4, No. 3, 182–190 (1969).
E.G. Gol'shtein, “Dual problems of convex and fractional-convex programming in functional spaces,” in: Studies in Mathematical Programming [in Russian], Nauka, Moscow (1968), pp. 10–108.
R.J. Duffin, “Infinite programs,” in: Linear Inequalities and Related Systems, Princeton University Press, Princeton (1956).
V.L. Levin, “Conditions for an extremum in infinite-dimensional linear problems with operator constraints,” in: Studies in Mathematical programming [in Russian], Nauka, Moscow (1968), pp. 159–197.
K. Fan, “On systems of linear inequalities,” in: Linear Inequalities and Related Systems, Princeton University Press, Princeton (1956).
N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Interscience Publishers (1957).
L.A. Lyusternik and V.I. Sobolev, Elements of Functional Analysis [in Russian], Nauka, Moscow (1965).
Additional information
Translated from Kibernetika, No. 3, pp. 35–46, May–June, 1971.
Rights and permissions
About this article
Cite this article
Pshenichnyi, B.N., Nenakhov, E.I. Necessary minimum conditions in problems with operator constraints. Cybern Syst Anal 7, 429–444 (1971). https://doi.org/10.1007/BF01070452
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01070452