Open AccessAbout the relaxed cocoercivity and the convergence of the proximal point algorithm
Author(s) -
Abdellatif Moudafi,
Zhenyu Huang
Publication year - 2013
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.03.014
Subject(s) - mathematics , convergence (economics) , lipschitz continuity , algorithm , point (geometry) , mathematical optimization , pure mathematics , geometry , economics , economic growth
The aim of this paper is to study the convergence of two proximal algorithms via the notion of (α,r)-relaxed cocoercivity without Lipschitzian continuity. We will show that this notion is enough to obtain some interesting convergence theorems without any Lipschitz-continuity assumption. The relaxed cocoercivity case is also investigated