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

Burke, Goldstein, Tseng, and Ye (Ref. 1) have presented an interesting inte rior-paint algorithm for a class of smooth convex minimax problems. They ha ve also presented a complexity analysis leading to a worst-case bound;on th e 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.