A Distributed First-Order Optimization Method for Strongly Concave-Convex Saddle-Point Problems

In this paper, we propose a first-order optimization method for solving saddle-point problems when the data is distributed over a strongly connected weight-balanced network of nodes. Our solution is based on the gradient descent-ascent where each node iteratively computes partial gradients of its local cost function to implement the corresponding steps. The proposed method further uses gradient tracking for both de-scent and ascent updates to tackle the local versus global cost gaps. We show that the proposed method converges linearly to the unique saddle-point when the global problem is strongly concave-convex. The numerical experiments il-lustrate the performance comparison of the proposed method with related work for different classes of problems.