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In this paper, we study the gradient descent-ascent method for convex-concavesaddle-point problems. We derive a new non-asymptotic global convergence ratein terms of distance to the solution set by using the semidefinite programmingperformance estimation method. The given convergence rate incorporates mostparameters of the problem and it is exact for a large class of stronglyconvex-strongly concave saddle-point problems for one iteration. We alsoinvestigate the algorithm without strong convexity and we provide somenecessary and sufficient conditions under which the gradient descent-ascentenjoys linear convergence.

Convergence rate analysis of the gradient descent-ascent method for convex-concave saddle-point problems