Singularly perturbed dynamics for distributed multi-agent optimization

Distributed algorithms are proposed to solve distributed optimization problems for a network of strongly connected agents in this paper. The proposed algorithms are based on a combination of a leader-following consensus protocol and the gradient descent method/primal-dual dynamics. In the leader-following consensus protocol, each agent acts as a virtual leader that provides its local measurements (i.e., local decision variables and gradient information) as reference signals to be followed by all the agents in the network. Based on the estimated information, the gradient methods are implemented. By utilizing the proposed methods, each agent produces an estimation on the minimization solution to the distributed optimization problem. Unconstrained distributed optimization problems are firstly addressed followed by distributed optimization problems with a balance constraint. Analytical convergence analysis is provided for both scenarios.