An Accelerated Distributed Proportional-Integral Method for Distributed Constrained Optimization

This letter addresses the distributed constrained optimization problem over multi-agent networks, where a group of agents collaboratively minimizes the average of their locally held objective functions, with the decision variables constrained within a global closed convex set. From a dynamic average consensus perspective, this letter proposes a new accelerated projection-based methods based on distributed proportional-integral (PI) framework, which requires communication of only one intermediate variable and avoids explicit gradient estimation, thereby reducing the communication burden compared to existing approaches that rely on gradient tracking techniques. To accelerate convergence, heavy-ball momentum terms are incorporated. Under smooth and strongly convex function assumptions, the proposed approach is demonstrated to converge linearly.