Distributed saddle-point seeking via a continuous-time multi-agent system

This paper presents a continuous-time multi-agent system for seeking constrained saddle-points in a distributed manner. In the system, two groups of agents are employed for computing the two state vectors in a saddle-point, respectively. Each agent seeks for consensus with the agents in the same group, and simultaneously optimizes its local objective functions by competing with the agents in the opposite group. In addition, a projection operator is introduced into the dynamics of each agent for dealing with bounded constraints. It is shown that the proposed system is convergent to a saddle-point of the given convex-concave objective function under connected and undirected communication graph. Finally, numerical simulation results are provided to substantiate the effectiveness of the proposed system.