Geodesic
Necessary optimality conditions in an abnormal optimization problem with equality constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1363-1368

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An abnormal minimization problem with equality constraints and a finite-dimensional image is examined. Second-order necessary conditions for this problem are given that strengthen previously known results. 
@article{ZVMMF_2006_46_8_a2,
     author = {A. V. Arutyunov and D. Yu. Karamzin},
     title = {Necessary optimality conditions in an abnormal optimization problem with equality constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1363--1368},
     publisher = {mathdoc},
     volume = {46},
     number = {8},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a2/}
}
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A. V. Arutyunov; D. Yu. Karamzin. Necessary optimality conditions in an abnormal optimization problem with equality constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1363-1368. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a2/