Distributed Convex Optimization Consensus in Multi-Agent Network Subject to Equality Constraints

By employing the Lyapunov direct method, this article investigated the distributed convex optimization consensus problem for multi-agent network subject to equality constraints, where each agent is comprised with an individual objective function which is coercive and convex. More specifically, a novel optimization consensus algorithm based on the gradient projection operator and the method of exploiting penalty is proposed. Furthermore, it is proved that for any initial state, the algorithm can achieve the consensus, and in the meanwhile reach the minimum of the aggregate objective functions within the constraint set. At last, a numerical example is provided to validate the effectiveness of the proposed optimization consensus algorithm.