Incremental Delayed Subgradient Method for Decentralized Nonsmooth Convex–Concave Minimax Optimization

In this paper, we propose an incremental-type subgradient scheme for solving a nonsmooth convex–concave minimax optimization problem in the setting of Euclidean spaces. We investigate convergence results by deriving an upper bound for the absolute value of the difference between the function value of the averaged iterates and the saddle value, provided that the step size is a constant. By assuming that the step-size sequence is diminishing, we prove the convergences of both the averaged sequence of function values and the sequence of function values of averaged iterates to the saddle value. Finally, we also show some numerical examples for illustrating the obtained theoretical result.