Extragradient and extrapolation methods with generalized Bregman distances for saddle point problems

In this paper, we introduce two Bregman-type algorithmic frameworks to generalize the extragradient and extrapolation methods. With help of relative Lipschitzness Bregman distance tool, iteration properties proposed are analyzed. As applied smooth convex-concave saddle point problems, our theory rediscovers main results in Mokhtari et al. (2020) [14] for wider under weaker assumptions via a conceptually different approach.