On the ChvtalGomory closure of a compact convex set
In this paper, we show that the ChvtalGomory closure of any compact convex set is a rational polytope. This resolves an open question of Schrijver (Ann Discret Math 9:291296, 1980) for irrational polytopes, and generalizes the same result for the case of rational polytopes (Schrijver in Ann Discret Math 9:291296, 1980), rational ellipsoids (Dey and Vielma in IPCO XIV, Lecture Notes in Computer Science, vol 6080. Springer, Berlin, pp 327340, 2010) and strictly convex bodies (Dadush et al. in Math Oper Res 36:227239, 2011).
chvtalgomory closure compact sets 90c10 integer programming 90c25 convex programming