Geodesic
Necessary extremum conditions in the optimal control problem with state constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 7, pp. 1123-1150

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The optimal control problem with state constraints is examined. An alternative to the available approaches to the study of this problem is proposed. The maximum principle and second-order necessary conditions are proved. 
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     author = {D. Yu. Karamzin},
     title = {Necessary extremum conditions in the optimal control problem with state constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1123--1150},
     publisher = {mathdoc},
     volume = {47},
     number = {7},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_7_a1/}
}
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D. Yu. Karamzin. Necessary extremum conditions in the optimal control problem with state constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 7, pp. 1123-1150. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_7_a1/