Well Behaved Asymptotical Convex Functions
Jean-Pierre Crouzeix, A. Auslender · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 1989
In this paper, we introduce the class \mathcal F of proper closed convex functions for which satisfy the following property. “For all sequences \{x_n\} , \{c_n\} such that c_n \in ∂f(x_n) and \lim\limits_{n\rightarrow ∞}\: c_n = 0 we have \lim\limits_{n\rightarrow ∞}\: f(x_n) = \inf(f(x)\mid x\in \mathbb R^N) ” Characterizations and applications are then given.