Geodesic
Necessary conditions for a weak extremum in optimal control problems on an infinite time interval
Sbornik. Mathematics, Tome 34 (1978) no. 3, pp. 327-343 
Yu. I. Brodskii. Necessary conditions for a weak extremum in optimal control problems on an infinite time interval. Sbornik. Mathematics, Tome 34 (1978) no. 3, pp. 327-343. http://geodesic.mathdoc.fr/item/SM_1978_34_3_a2/
@article{SM_1978_34_3_a2,
     author = {Yu. I. Brodskii},
     title = {Necessary conditions for a~weak extremum in optimal control problems on an infinite time interval},
     journal = {Sbornik. Mathematics},
     pages = {327--343},
     year = {1978},
     volume = {34},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1978_34_3_a2/}
}
TY  - JOUR
AU  - Yu. I. Brodskii
TI  - Necessary conditions for a weak extremum in optimal control problems on an infinite time interval
JO  - Sbornik. Mathematics
PY  - 1978
SP  - 327
EP  - 343
VL  - 34
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1978_34_3_a2/
LA  - en
ID  - SM_1978_34_3_a2
ER  - 
%0 Journal Article
%A Yu. I. Brodskii
%T Necessary conditions for a weak extremum in optimal control problems on an infinite time interval
%J Sbornik. Mathematics
%D 1978
%P 327-343
%V 34
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1978_34_3_a2/
%G en
%F SM_1978_34_3_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

The work is concerned with an optimal control problem on an infinite time interval. A simple method of interpretating the Euler equation is given, which does not require the use of approximation theory. Necessary conditions for a weak extremum in the form of a local maximum principle are obtained. Bibliography: 9 titles.

[1] A. Ya. Dubovitskii, A. A. Milyutin, Neobkhodimye usloviya slabogo ekstremuma v obschei zadache optimalnogo upravleniya, izd-vo “Nauka”, Moskva, 1971

[2] A. Ya. Dubovitskii, A. A. Milyutin, “Zadachi na ekstremum pri nalichii ogranichenii”, ZhVM i MF, 5:3 (1965), 395–453 | Zbl

[3] L. A. Lyusternik, V. I. Sobolev, Elementy funktsionalnogo analiza, izd-vo “Nauka”, Moskva, 1965 | MR

[4] A. Ya. Dubovitskii, Integralnyi printsip maksimuma v obschei zadache optimalnogo upravleniya, dep. v VINITI, no. 2639–74

[5] Yu. I. Brodskii, Lokalnyi printsip maksimuma dlya nepreryvnykh i diskretnykh zadach optimalnogo upravleniya na beskonechnom intervale vremeni, dep. v VINITI, no. 2562-76

[6] Yu. I. Brodskii, Printsip maksimuma L. S. Pontryagina v obschei zadache optimalnogo upravleniya, dep. v VINITI, no. 850-77

[7] A. Ya. Dubovitskii, Integralnyi printsip maksimuma v obschei zadache optimalnogo upravleniya, Doktorskaya dissertatsiya, VTs AN SSSR, 1975

[8] A. Ya. Dubovitskii, A. A. Milyutin, “Neobkhodimye usloviya slabogo ekstremuma v zadachakh optimalnogo upravleniya so smeshannymi ogranicheniyami tipa neravenstva”, ZhVM i MF, 8,:4 (1968), 725–779 | Zbl

[9] E. Khille, R. Fillips, Funktsionalnyi analiz i polugruppy, IL, Moskva, 1962