Open Distributed Convex Optimization
Xiaoyu Wu, Jie Lin, Shanchan Jiang, Zhicheng Zhang, Yingxue Du, Yan Zhang · IEEE Transactions on Automatic Control · 2025
This paper investigates the distributed convex optimization problem where dimension of the feasible set is fluctuated. To address this, we formulate an open consensus algorithm that enables agents to join or leave at any time while seeking the optimal solution. By introducing an auxiliary variable to account for agent departures and incorporating a diminishing gradient descent scheme, we seek the Lyapunov-based method to establish conditions ensuring that consensus remains achievable and rigorously proving that agents aggregate to the optimal solution. Finally, we validate the proposed method and theoretical findings through both a numerical example and a practical instance.