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Rogak, E. D.; Scott-Thomas, J. F.

On necessary conditions for optimality in a Banach space. (English) Zbl 0274.49009

J. Math. Anal. Appl. 41, 44-53 (1973).
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Cited in 4 Documents

MSC:

49K27 Optimality conditions for problems in abstract spaces
49K20 Optimality conditions for problems involving partial differential equations
49K99 Optimality conditions
49J20 Existence theories for optimal control problems involving partial differential equations
49J27 Existence theories for problems in abstract spaces
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
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References:

[1] Cesari, L., Optimization with partial differential equations in Dieudonné-Rashevsky form and conjugate problems, Arch. Rational Mech. Anal., 33, 339-357 (1969) · Zbl 0182.20302
[2] Dieudonné, J., Foundations of Modern Analysis (1960), Academic Press: Academic Press New York · Zbl 0100.04201
[3] Egorov, A. I., Optimal control in Banach space, Math. Systems Theory, 1, 347-352 (1968) · Zbl 0171.05701
[4] Egorov, Yu, Necessary conditions for optimality in Banach space, Mat. Sbornik, T 64, No. 1, 79-101 (1964) · Zbl 0196.47301
[5] Hestenes, M., Calculus of Variations and Optimal Control Theory (1966), Wiley: Wiley New York · Zbl 0173.35703
[6] Lions, J., Optimal Control of Systems Governed by Partial Differential Equations (1971), Springer: Springer New York · Zbl 0203.09001
[7] Raitums, U., On an existence criterion for an analog of the maximum principle, Lat. Mat. Yr. book, 3, 283-290 (1968), Riga · Zbl 0209.16502
[8] Rogak, E. D.; Kazarinoff, N. D.; Scott-Thomas, J. F., Sufficient Conditions for Bang-Bang Control in Hilbert Space, J. Optimization Theory Appl., 5, 1-11 (1970) · Zbl 0177.12905
[9] Rozonoer, L., The Pontryagin maximum principle in the theory of optimal systems I, Automat. Remote Control, 20, 1320-1334 (1959)
[10] Smirnov, V. I., A Course in Higher Mathematics, Vol. 5 (1959), Moscow
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