Tuesday, October 27, 2015, 4:00 pm
Damek Davis, Department of Mathematics, University of California, Los Angeles .
A Three-Operator Splitting Scheme and its Optimization Applications
Abstract: For over 50 years, operator-splitting schemes have been used to solve PDE, feasibility problems, and more recently, large-scale problems in data analysis. Despite much development, it is known that most existing splitting schemes reduce to one of three basic schemes, each introduced between 15 and 36 years ago.
We introduce a new splitting scheme that extends the Douglas-Rachford and forward-backward splitting schemes to monotone inclusions with three operators, one of which is cocoercive. We discuss why this algorithm works, derive several special cases, including a simple three-block ADMM algorithm, and introduce an acceleration that achieves the optimal rate of convergence for strongly monotone inclusions. Finally, we discuss several applications and future research directions.