Cooperative-Competitive Multiagent Systems for Distributed Minimax Optimization Subject to Bounded Constraints

This paper presents continuous-time multiagent systems for distributed minimax optimization subject to bounded constraints. All agents in the system are divided into two groups for minimization and maximization. The multiagent system features competitive inter-group interactions and cooperative intragroup interactions, both of which based on the output information of agents. First, a proportional-integral intragroup interaction rule is utilized for consensus within each group in the system. With this interaction rule, the system is proved to be convergent to an optimal solution to the problem, under certain requirement on the inter-group interactions. Second, another discontinuous intragroup interaction rule is introduced. It is proved that the system with such an interaction is still convergent to an optimal solution if the proportional gain exceeds a derived lower bound without previous requirement on the inter-group interactions. Furthermore, exponential convergence to an optimal solution is proved if each local objective function is strongly convex-concave. As a special case, the systems are further applied for distributed optimization. Finally, simulation results are presented to substantiate the
theoretical results.