Design and Analysis of Distributed Multi-Agent Saddle Point Algorithm Based on Gradient-Free Oracle

In the paper, we are interested in one convex-concave function problem in network applications. Motivated by the saddle-point subgradient methods, we deal with a kind of saddle-point problem for multi-agent systems whose objective function for the underlying issue must be non-smooth but Lipschitz continuous. With the convex constrain set and global convex inequality constraints, we present a kind of distributed gradient-free algorithm in order to solve the issue of multi-agent convex-concave optimization. Under Slater’s condition, We give the results of convergence rate and the effect of smoothing parameters on error bounds.