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The proximal map is the key step in gradient-type algorithms, which have become prevalent in large-scale high-dimensional problems. For simple functions this proximal map is available in closed-form while for more complicated functions it can become highly nontrivial. Motivated by the need of combining regularizers to simultaneously induce different types of structures, this paper initiates a systematic investigation of when the proximal map of a sum of functions decomposes into the composition of the proximal maps of the individual summands. We not only unify a few known results scattered in the literature but also discover several new decompositions obtained almost effortlessly from our theory.
Author Information
Yao-Liang Yu (University of Waterloo)
Related Events (a corresponding poster, oral, or spotlight)
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2013 Oral: On Decomposing the Proximal Map »
Fri. Dec 6th 07:00 -- 07:20 PM Room Harvey's Convention Center Floor, CC
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