Decentralized Optimization for Graph-Structured Nonlinear Programs
Analysis
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.
Key Takeaways
- •Proposes MP-Jacobi, a decentralized framework for graph-structured nonlinear programs.
- •Combines message passing and Jacobi block updates for parallel updates and single-hop communication.
- •Provides convergence guarantees and explicit rates for strongly convex objectives.
- •Develops surrogate methods to reduce computational complexity.
- •Extends the method to hypergraphs.
“MP-Jacobi couples min-sum message passing with Jacobi block updates, enabling parallel updates and single-hop communication.”