Mathematical Programming

, Volume 145, Issue 1–2, pp 327–348

On the Chvátal–Gomory closure of a compact convex set

  • Daniel Dadush
  • Santanu S. Dey
  • Juan Pablo Vielma
Full Length Paper Series A


In this paper, we show that the Chvátal–Gomory closure of any compact convex set is a rational polytope. This resolves an open question of Schrijver (Ann Discret Math 9:291–296, 1980) for irrational polytopes, and generalizes the same result for the case of rational polytopes (Schrijver in Ann Discret Math 9:291–296, 1980), rational ellipsoids (Dey and Vielma in IPCO XIV, Lecture Notes in Computer Science, vol 6080. Springer, Berlin, pp 327–340, 2010) and strictly convex bodies (Dadush et al. in Math Oper Res 36:227–239, 2011).


Chvátal–Gomory closure Compact sets 

Mathematics Subject Classification

90C10 Integer programming 90C25 Convex programming 

Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2013

Authors and Affiliations

  • Daniel Dadush
    • 1
  • Santanu S. Dey
    • 1
  • Juan Pablo Vielma
    • 2
    • 3
  1. 1.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Sloan School of ManagementMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.Department of Industrial EngineeringUniversity of PittsburghCambridgeUSA

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