Distributed Primal-Dual Mirror Dynamics for Constraint-Coupled Optimization

In this work, a class of distributed constrained-coupled optimization problems is studied. A primal-dual mirror dynamics is proposed, which is a generalization of the classical primal-dual gradient dynamics. However, the primal-dual mirror dynamics cannot be implemented distributedly, due to the existence of the coupled equality constraint. Therefore, a distributed primal-dual mirror dynamics is further designed and its convergence is proved under the assumption that local objectives are strictly convex and the communication topology among agents is undirected and connected. In the end, numerical simulations are taken to verify the theoretical analysis.