Title	The Douglas-Rachford algorithm in the possibly inconsistent case
Creator	Moursi, Walaa
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2017-09-19T11:14
Description	The Douglas–Rachford algorithm is a very popular splitting technique for finding a zero of the sum of two maximally monotone operators. The behaviour of the algorithm remains mysterious in the general inconsistent case, i.e., when the sum problem has no zeros. However, more than a decade ago, it was shown that in the (possibly inconsistent) convex feasibility setting, the shadow sequence remains bounded and its weak cluster points solve a best approximation problem. In this talk, we advance the understanding of the inconsistent case significantly by presenting a complete proof of the full weak convergence in the convex feasibility setting. We also provide linear rate of convergence and strong convergence in special cases.
Extent	37 minutes
Subject	Mathematics; Operations research, mathematical programming; Operator theory; Control/optimization/operation research
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: UBC
Series	BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))
Date Available	2018-03-24
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0364446
URI	http://hdl.handle.net/2429/64916
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Graduate
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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The Douglas-Rachford algorithm in the possibly inconsistent case Moursi, Walaa

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