Geodesic
Necessary optimality conditions for abnormal problems with geometric constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 3, pp. 364-375

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The abnormal minimization problem with a finite-dimensional image and geometric constraints is examined. In particular, inequality constraints are included. Second-order necessary conditions for this problem are established that strengthen previously known results. 
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     author = {A. V. Arutyunov and D. Yu. Karamzin},
     title = {Necessary optimality conditions for abnormal problems with geometric constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_3_a1/}
}
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A. V. Arutyunov; D. Yu. Karamzin. Necessary optimality conditions for abnormal problems with geometric constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 3, pp. 364-375. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_3_a1/