Distributed Convergence to Saddle-Points Over General Directed Multi-Agent Networks

In this paper, distributed saddle-points seeking problem is addressed in the scenario of general directed communication graphs, which does not require the weight-balanced condition. By utilizing the push-sum technique, a continuous-time multi-agent system is designed for computing a saddle point of a given convex-concave objective function in a distributed manner. It is proven that the proposed system is convergent to a saddle-point under a series of time-varying strongly connected communication graphs. Finally, numerical simulation results are provided to substantiate the effectiveness of the proposed system.