An asymptotic inclusion speed for the Douglas-Rachford splitting method in Hilbert spaces
Yunda Dong (ydongzzu.edu.cn)
Abstract: In this paper, we consider the Douglas-Rachford splitting method for monotone inclusion in Hilbert spaces. It can be implemented as follows: from the current iterate, first use forward-backward step to get the intermediate point, then to get the new iterate. Generally speaking, the sum operator involved in the Douglas-Rachford splitting takes the value of every intermediate point as a set. Our goal of this paper is to show that such generated set-valued sequence asymptotically includes the origin and the corresponding asymptotic inclusion speed remains desirable if the forward splitting is further Lipschitz continuous.
Keywords: Monotone inclusion; Douglas-Rachford splitting; Proximal point algorithm; Asymptotic inclusion speed.
Category 1: Convex and Nonsmooth Optimization (Convex Optimization )
Entry Submitted: 12/21/2014
Modify/Update this entry
|Visitors||Authors||More about us||Links|
Search, Browse the Repository
Give us feedback
|Optimization Journals, Sites, Societies|