A New Regularized Consensus Perspective for Distributed Optimization

In this article, a new regularized consensus perspective is presented for solving distributed optimization problems among a network of heterogeneous linear dynamic agents. The distributed optimization problem can be viewed as a consensus problem, in which the consensus direction should be regularized to optimize the sum of the agents' objective functions. Based on this idea, a regularized consensus mapping is defined, by which a continuous-time distributed optimization algorithm is established and analyzed for heterogeneous linear dynamic agents. It is shown that the outputs of the linear dynamic agents can evolve to the distributed optimization solution. Moreover, a dynamic event-triggered scheme is proposed to achieve communication-efficient distributed optimization by reducing the communication costs among neighboring agents. Numerical simulation examples are provided to verify the effectiveness of the proposed methods.