Consensus based constrained optimization for multi-agent systems

By introducing multi-agent systems, a consensus based distributed optimization algorithm is considered in this paper. The state of each agent is to be controlled to reach a consensus on the global optimal set. From control point of view, the control input of each agent is designed based on neighbours´ state information and local cost functions. Necessary and sufficient conditions on the convergence of the whole system are given in terms of graph connectivity and balancedness, as well as the persistence of the decaying step size. The convergence rate is given under some general assumptions. Last, some numerical examples are given to show the effectiveness of the control protocol.