An Accelerated Gradient-Dually-Concave Method for the Smooth and Convex-Concave Saddle Point Problem

Accelerated Primal-Dual Gradient Method for Smooth and Convex-Concave Saddle-Point Problems with Bilinear Coupling

In this paper we study a convex-concave saddle-point problem where and are smooth and convex functions.We propose an accelerated primal-dual gradient method for solving this problem which (i) achieves an optimal linear convergence rate in the strongly-convex-strongly-concave regime matching the lower complexity bound(zhang et al., 2021) and (ii) achieves an accelerated linear convergence rate in the case when only one of the functions and is strongly convexor even none of them are.Finally, we obtain a linearly-convergent algorithm for the general smooth and convex-concave saddle point problem without requirement of strong convexity or strong concavity.