The Douglas-Rachford algorithm and operator splitting strategies
Russell Luke
University of Delaware

Abstract:The Douglas-Rachford algorithm (1956) is an iterative method for solving Poisson's equation. It has been generalized to operator splitting strategies for solving generalized inclusions of maximally monotone operators. With the help of a little convex analysis, this seemingly unintuitive algorithm can be shown to be a generalization of many more familiar algorithms, like the method of steepest descent and alternating projections.

We review the origins of the Douglas-Rachford algorithm and survey its modern form with applications. This talk is intended to provide the necessary background for Jonathan Eckstein's talk in the PDE seminar on Nov. 19.