The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle

Understand

The Douglas-Rachford splitting algorithm is a classical optimization method that has found many applications.

• When specialized to two normal cone operators, it yields an algorithm for finding a point in the intersection of two convex sets.
• This method for solving feasibility problems has attracted a lot of attention due to its good performance even in nonconvex settings.
• In this paper, we consider the Douglas-Rachford algorithm for finding a point in the intersection of two subspaces.