A Framework for Decentralised Resolvent Splitting

Decentralised optimisation is typically concerned with problems having objective functions with finite-sum structure that are distributed over a network. Although there are several decentralised algorithms in the literature for solving minimisations problems with the aforementioned form, relatively few of these generalise to the abstraction of monotone inclusions. In this work, we address this by developing a new framework for decentralised resolvent splitting for finding a zero in the sum of finitely many set-valued monotone operators over regular networks. Our framework also simplifies and extends non-decentralised splitting algorithms in the literature.