  In this paper we consider solving saddle point problems using two variants of
Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient
Descent Ascent (OGDA) methods. We show that both of these algorithms admit a
unified analysis as approximations of the classical proximal point method for
solving saddle point problems. This viewpoint enables us to develop a new
framework for analyzing EG and OGDA for bilinear and strongly convex-strongly
concave settings. Moreover, we use the proximal point approximation
interpretation to generalize the results for OGDA for a wide range of
parameters.
