Mathematical Programs for Belief Propagation and Consensus

This paper develops methods of distributed Bayesian hypothesis tests for fault detection and diagnosis that are based on belief propagation and optimization in graphical models. The main challenges in developing distributed statistical estimation algorithms are i) difficulties in ensuring convergence and consensus for solutions of distributed inference problems, ii) increasing computational costs due to lack of scalability, and iii) communication constraints for networked multi-agent systems. To cope with those challenges, this manuscript considers i) belief propagation and optimization in graphical models of complex distributed systems, ii) decomposition methods of optimization for parallel and iterative computations, and iii) distributed decision-making protocols.