On the Properties of Convex Functions over Open Sets

Autor:	Drori, Yoel
Rok vydání:	2018
Předmět:	Mathematics - Optimization and Control Mathematics - Functional Analysis Mathematics - Metric Geometry 26B25 (Primary) 90C25 52A20 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We consider the class of smooth convex functions defined over an open convex set. We show that this class is essentially different than the class of smooth convex functions defined over the entire linear space by exhibiting a function that belongs to the former class but cannot be extended to the entire linear space while keeping its properties. We proceed by deriving new properties of the class under consideration, including an inequality that is strictly stronger than the classical Descent Lemma. Comment: Minor update to Theorem 3.2
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1812.02419 Zobrazit plný text záznamu View this record from Arxiv