Distributed Proximal Algorithms for Multiagent Optimization With Coupled Inequality Constraints

This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum locally accessible convex functions subject feasible set constraint coupled inequality constraints whose information is only partially each agent. For this problem, proximal-based algorithm, called proximal primal-dual (DPPD) proposed based on celebrated centralized point algorithm. It shown that algorithm can lead optimal solution with general stepsize, which diminishing non-summable, but not necessarily square-summable, saddle-point running evaluation error vanishes proportionally $O(1/\sqrt{k})$, $k>0$ iteration number. Finally, simulation example presented corroborate effectiveness