Abstract:
In this talk, we examine some results regarding the permissible structure of fixed point algorithms for finding a zero in the sum of $n\geq 2$ maximally monotone operators using their resolvents. The standard approach to this problem involves reformulating as an equivalent two operator inclusion within an $n$-fold Cartesian product space and applying the Douglas--Rachford algorithm. However, recent progress has revealed that there are actually a number alternative algorithms that do not directly rely on the standard product space formulation. In this talk, we will consider the conditions needed for convergence of a general resolvent splitting algorithm. The framework includes many of these new alternatives algorithms as special cases as well as greatly simplifying their convergence proofs.