Supplementary Material for: Improved Algorithms for Convex-Concave Minimax Optimization 1 Some Useful Properties In this section, we review some useful properties of functions in F (m

Then, we have that 1. y Fact 2. Let z:= [ x; y ] and z This can be easily proven using the AM-GM inequality. Fact 3. Let z:= [ x; y ] R It is a crucial building block for the algorithms in this work. The following classical theorem holds for AGD. We will start by giving a precise statement of Algorithm 1.Algorithm 1 Alternating Best Response (ABR)Require: g (,), Initial point z The basic idea is the following. The following two lemmas about the inexact APP A algorithm follow from the proof of Theorem 4.1 [ Here we provide their proofs for completeness.