Geodesic
A~weakened variant of the law of Lagrange multipliers in a~Banach space
Matematičeskie zametki, Tome 21 (1977) no. 2, pp. 223-228.

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The notion of a quasicritical mapping of a Banach space into another Banach space is introduced and a theorem on the equivalence of this notion (under some additional assumptions) to a weakened variant of the law of the Lagrange multipliers in the form of an inequality is proved 
@article{MZM_1977_21_2_a10,
     author = {M. F. Sukhinin},
     title = {A~weakened variant of the law of {Lagrange} multipliers in {a~Banach} space},
     journal = {Matemati\v{c}eskie zametki},
     pages = {223--228},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a10/}
}
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M. F. Sukhinin. A~weakened variant of the law of Lagrange multipliers in a~Banach space. Matematičeskie zametki, Tome 21 (1977) no. 2, pp. 223-228. http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a10/