Geodesic
Geometric approach to finding the conditional extrema
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 26 (2020) no. 4, pp. 244-254

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In this paper, we give a geometric interpretation and a geometric proof of the necessary condition for the existence of a constrained extremum. The presented approach can be applied to finding constrained extrema of nondifferentiable functions (i.e., when Lagrange's method of undetermined multipliers is not applicable in the “classical” form). The following examples are considered: the inequality of arithmetic and geometric means, Young's inequality for products, and Jensen's inequality.
Keywords: interpolation; divided difference; spline; derivative. 
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     title = {Geometric approach to finding the conditional extrema},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2020_26_4_a16/}
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D. S. Telyakovskii; S. A. Telyakovskii. Geometric approach to finding the conditional extrema. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 26 (2020) no. 4, pp. 244-254. http://geodesic.mathdoc.fr/item/TIMM_2020_26_4_a16/