Geodesic
Second order tangent vectors to sets and minimality conditions for points of subsets of ordered normed spaces
Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 35-47.

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Using the extended second order tangent cone as a local approximation of a subset at a neighborhood of the point under consideration, we obtain both necessary and sufficient (in finite-dimensional spaces) conditions for locally minimal points of subsets of ordered normed spaces. The gap between necessary and sufficient conditions obtained in the paper is irremovable in the setting of second order local approximations. 
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V. V. Gorokhovik. Second order tangent vectors to sets and minimality conditions for points of subsets of ordered normed spaces. Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 35-47. http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a4/

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