Abstract: This paper investigates the distributed consensus optimization problem with coupled constraints, where the objective function is the sum of the local objective functions of each agent, and the decision variables are subject to coupled nonlinear constraints.  All agents exchange information with one another to ensure consensus on the decision variables and achieve optimality. To address this problem, a distributed proximal method of multipliers is proposed by combining the centralized proximal method of multipliers and the distributed gradient-tracking algorithm. It is shown that this algorithm converges to the optimal solutions of both primal and dual problems for any constant step size. Notably, the algorithm can handle general coupled constraints, requiring only closedness and convexity assumptions.

Key words: Distributed optimization;Constraint-coupled optimization;Proximal method of multipliers, Gradient-tracking