Distributed Constrained Minimax Optimization Based on Zero-Sum Games for Multi-agent Systems

In this paper, the constrained minimax optimization problems are investigated in a distributed manner. Under the framework of multi-agent systems, there are two clusters are responsible for computing two vectors to minimize and maximize the global objective function, which can be considered as zero-sum games. In this scenario, agents can communicate with neighbors over their communication topologies to achieve consensus. Meanwhile, only partial state information of another cluster can be obtained. We design a new algorithm to deal with this problem by utilizing projection operator and Lagrangian multiplier method. Through further analysis, we prove that the algorithm can converge to an optimal solution while certain sufficient conditions hold. Lastly, we present a simulation example to show the validity of the algorithm.