Distributed Augmented Primal-Dual Algorithm for Multi-Agent Constrained Optimization

This paper deals with the distributed optimization problem while respecting coupled affine equality constraints. Resorting to the augmented Lagrangian function, a novel distributed augmented primal-dual algorithm is developed by virtue of the gradient tracking and dynamic consensus mechanisms. Based on the carefully constructed Lyapunov function, it is proved that the proposed algorithm can achieve linear convergence and an exact upper bound on the stepsize is given. Finally, a numerical example is presented to corroborate the effectiveness of the designed algorithm.