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On Decomposing the Proximal Map
Yao-Liang Yu

Fri Dec 06 11:00 AM -- 11:20 AM (PST) @ Harvey's Convention Center Floor, CC

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)

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