A Distributed Primal–Dual Push-Sum Algorithm on Open Multiagent Networks

This article addresses distributed constrained convex optimization in open multiagent systems characterized by dynamic and unpredictable changes in their structural components and active participants. Such systems, often found in many networked infrastructures, have an openness property, wherein the configuration and the number of active agents vary significantly. This article considers a distributed online algorithm to estimate a dynamic optimal strategy that minimizes a dynamic regret and a constraint violation, quantifying the algorithm's performance concerning the cost optimality and conformity to the constraints. Each active agent iteratively updates its local variables through a consensus-based primal–dual algorithm, integrating information from neighboring agents. We evaluate the algorithm's performance by showing sublinear bounds in dynamic regret and the constraint violation. We also provide empirical validation via a numerical simulation of an economic dispatch problem in a power network.