On complexity of the translational-cut algorithm for convex minimax problems

Burke, Goldstein, Tseng, and Ye (Ref. 1) have presented an interesting interior-paint algorithm for a class of smooth convex minimax problems. They have also presented a complexity analysis leading to a worst-case bound;on the total work necessary to obtain a solution within a prescribed tolerance. In this paper, we present refinements to the analysis of Burke et al. which show that the resulting complexity bound can be worse than those for other algorithms available at the time Ref. 1 was published.