Analysis Seminar

Splitting Two Monotone Operators Goes a Long Way

Speaker: Patrick Louis Combettes, Laboratoire Jacques-Louis Lions, Université Paris 6

Location: Warren Weaver Hall 1302

Date: Thursday, October 3, 2013, 11 a.m.


A basic problem in applied mathematics is to find a zero of the sum of two monotone operators. The main splitting algorithms for solving this problem were essentially developed in the late 1970s. We show that, by bringing into play duality tools and product formulations, these fundamental splitting principles can be exploited to solve considerably more complex multicomponent composite inclusion problems efficiently. Applications to machine learning, PDEs, and image recovery will be discussed.