Title	On Decomposing the Proximal Map
Creator	Yu, Yaoliang
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2017-09-19T13:00
Description	The proximal map has played a significant role in convex analysis and various splitting algorithms. For "simple" functions this proximal map is available in closed-form while in general it needs to be computed by iterative numerical algorithms hence being inefficient. Motivated by applications in machine learning, we study when the proximal map of a sum of functions decomposes into the composition of the (simple) proximal maps of the individual summands. We present a simple sufficient condition and we demonstrate its surprising effectiveness by unifying and extending several results in seemingly unrelated fields. We end our discussion with a few open directions.
Extent	35 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: University of Waterloo
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	10.14288/1.0364448
URI	http://hdl.handle.net/2429/64918
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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On Decomposing the Proximal Map Yu, Yaoliang

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