Convex-Concave Interpolation and Application of PEP to the Bilinear-Coupled Saddle Point Problem

In this paper we present interpolation conditions for several important convex-concave function classes: nonsmooth convex-concave functions, conditions for difference of strongly-convex functions in a form that contains oracle information exclusively and smooth convex-concave functions with a bilinear coupling term. Then we demonstrate how the performance estimation problem approach can be adapted to analyze the exact worst-case convergence behavior of firstorder methods applied to composite bilinear-coupled min-max problems. Using the performance estimation problem approach, we estimate iteration complexities for several first-order fixed-step methods, Sim-GDA and Alt-GDA, which are applied to smooth convex-concave functions with a bilinear coupling term.