Randomized Distributed Strategy for a Class of Convex Optimization With Coupling Constraints

In this paper, we consider a class of constrained convex optimization problems, where the global cost function is defined as the sum of agents' individual cost functions. Both local and coupling global constraints involving all agents' states are considered and allowed to be nonlinear. To handle the separable cost function, however, not separable constraints, we propose a randomized distributed algorithm based on the regularized penalty method. In the designed algorithm, each agent firstly estimates the global constraint and its gradient with respect to itself with the help of a properly designed distributed estimator of global states via only local information exchange with its neighbours. Then each agent performs the update of its decision variable at each iteration followed by optimization steps of its local cost function, coupling global constraint, and randomly considered local inequality/equation constraints for memory saving. It is proved that with the proposed randomized distributed algorithm, the decision variables of the agents converge to the optimal set of the approximated problem based on the penalty method almost surely. Simulation results of multi-agent systems are provided to verify the theoretical results.