Geodesic
A conditional extremum necessary condition in terms of local algebras
Trudy Instituta matematiki, Tome 19 (2011) no. 2, pp. 3-6.

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We prove a necessary condition for local extremum in the classical optimization problem with equality constraints. It states that at the point of extremum the dimension of the local algebra associated with the problem cannot be odd. 
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V. I. Bakhtin. A conditional extremum necessary condition in terms of local algebras. Trudy Instituta matematiki, Tome 19 (2011) no. 2, pp. 3-6. http://geodesic.mathdoc.fr/item/TIMB_2011_19_2_a0/

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