Decentralized Optimization for Graph-Structured Nonlinear Programs

This paper introduces MP-Jacobi, a novel decentralized framework for solving nonlinear programs defined on graphs or hypergraphs. The approach combines message passing with Jacobi block updates, enabling parallel updates and single-hop communication. The paper's significance lies in its ability to handle complex optimization problems in a distributed manner, potentially improving scalability and efficiency. The convergence guarantees and explicit rates for strongly convex objectives are particularly valuable, providing insights into the method's performance and guiding the design of efficient clustering strategies. The development of surrogate methods and hypergraph extensions further enhances the practicality of the approach.