Volume 71, August 2021FGS’2019 - 19th French-German-Swiss conference on Optimization
|Page(s)||114 - 120|
|Published online||01 September 2021|
Sensitivity of the “intermediate point” in the mean value theorem: an approach via the Legendre-Fenchel transformation
Institut de Mathématiques, Université Paul Sabatier, 118 route de Narbonne, Toulouse ( France )
We study the sensitivity, essentially the differentiability, of the so-called “intermediate point” c in the classical mean value theorem we provide the expression of its gradient ∇c(d,d), thus giving the asymptotic behavior of c(a, b) when both a and b tend to the same point d. Under appropriate mild conditions on f, this result is “universal” in the sense that it does not depend on the point d or the function f. The key tool to get at this result turns out to be the Legendre-Fenchel transformation for convex functions.
© The authors. Published by EDP Sciences, SMAI 2021
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