  We study the iteration complexity of the optimistic gradient descent-ascent
(OGDA) method and the extra-gradient (EG) method for finding a saddle point of
a convex-concave unconstrained min-max problem. To do so, we first show that
both OGDA and EG can be interpreted as approximate variants of the proximal
point method. This is similar to the approach taken in [Nemirovski, 2004] which
analyzes EG as an approximation of the `conceptual mirror prox'. In this paper,
we highlight how gradients used in OGDA and EG try to approximate the gradient
of the Proximal Point method. We then exploit this interpretation to show that
both algorithms produce iterates that remain within a bounded set. We further
show that the primal dual gap of the averaged iterates generated by both of
these algorithms converge with a rate of $\mathcal{O}(1/k)$. Our theoretical
analysis is of interest as it provides a the first convergence rate estimate
for OGDA in the general convex-concave setting. Moreover, it provides a simple
convergence analysis for the EG algorithm in terms of function value without
using compactness assumption.
