About the relaxed cocoercivity and the convergence of the proximal point algorithm
Moudafi, A., Huang, Z. (2013). About the relaxed cocoercivity and the convergence of the proximal point algorithm. EKB Journal Management System, 21(2), 281-284. doi: 10.1016/j.joems.2013.03.014
Abdellatif Moudafi; Zhenyu Huang. "About the relaxed cocoercivity and the convergence of the proximal point algorithm". EKB Journal Management System, 21, 2, 2013, 281-284. doi: 10.1016/j.joems.2013.03.014
Moudafi, A., Huang, Z. (2013). 'About the relaxed cocoercivity and the convergence of the proximal point algorithm', EKB Journal Management System, 21(2), pp. 281-284. doi: 10.1016/j.joems.2013.03.014
Moudafi, A., Huang, Z. About the relaxed cocoercivity and the convergence of the proximal point algorithm. EKB Journal Management System, 2013; 21(2): 281-284. doi: 10.1016/j.joems.2013.03.014

About the relaxed cocoercivity and the convergence of the proximal point algorithm

Journal of the Egyptian Mathematical Society
Volume 21, Issue 2, August 2013, Pages 281-284    PDF (346.57 K)
Document Type: Review article
DOI: 10.1016/j.joems.2013.03.014
Authors
Abdellatif Moudafi* 1; Zhenyu Huang2
1French West Indies University, Ceregmia-Scientific Department, 97200 Schelcher, Martinique, France
2Department of Mathematics, Nanjing University, Nanjing 210093, PR China
Abstract
The aim of this paper is to study the convergence of two proximal algorithms via the
notion of (a, 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.
Keywords
Relaxed cocoercivity; Relaxed monotonicity; Proximal point algorithm; Strong convergence; Variational inequalities
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