Distributed convex optimization based on ADMM and belief propagation methods

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AbstractWe consider a distributed convex optimization problem in which a connected network of agents collaboratively seeks to minimize the sum of their local objective functions over a common decision variable. We propose a new distributed optimization method in the Alternating Direction Method of Multipliers (ADMM) framework, But our method combines the celebrated Belief Propagation(BP) algorithm and relaxation iteration method to achieve distributed optimization. Numerical simulation shows that our proposed algorithms have good convergence speed. We also discuss the trade‐off between the convergence rate and the required communication and computational complexities.