  We show that the primal-dual gradient method, also known as the gradient
descent ascent method, for solving convex-concave minimax problems can be
viewed as an inexact gradient method applied to the primal problem. The
gradient, whose exact computation relies on solving the inner maximization
problem, is computed approximately by another gradient method. To model the
approximate computational routine implemented by iterative algorithms, we
introduce the notion of dynamic inexact oracles, which are discrete-time
dynamical systems whose output asymptotically approaches the output of an exact
oracle. We present a unified convergence analysis for dynamic inexact oracles
realized by general first-order methods and demonstrate its use in creating new
accelerated primal-dual algorithms.
