In this note we provide a simple proof of some properties enjoyed by convex functions having the engulfing property. In particular, making use only of results peculiar to convex analysis, we prove that differentiability and strict convexity are conditions intrinsic to the engulfing property.
Calogero, A., Pini, R. (2020). The engulfing property from a convex analysis viewpoint. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 187(2), 408-420 [10.1007/s10957-020-01755-1].
The engulfing property from a convex analysis viewpoint
Calogero, AG;Pini, R
2020
Abstract
In this note we provide a simple proof of some properties enjoyed by convex functions having the engulfing property. In particular, making use only of results peculiar to convex analysis, we prove that differentiability and strict convexity are conditions intrinsic to the engulfing property.
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