Distributed Optimization with Sheaf Homological Constraints
Jakob Hansen, Robert Ghrist · 2019
In this paper we introduce a new class of local linear operators on graphs, the sheaf Laplacians, which provide drop-in replacements for graph Laplacians in distributed algorithms. These operators can enforce more general constraints on data distributed in a network than those given by the graph Laplacian. The constraints for such optimization problems can be framed in the context of sheaf cohomology, leading to a description of this framework as distributed optimization with homological constraints. We formulate a representative problem, elucidate its solution with sheaf Laplacians, and give illustrative examples of potential applications.