Mathematical Programming

, Volume 172, Issue 1–2, pp 329–349 | Cite as

Minimal cut-generating functions are nearly extreme

  • Amitabh Basu
  • Robert Hildebrand
  • Marco Molinaro
Full Length Paper Series B


We study continuous (strongly) minimal cut generating functions for the model where all variables are integer. We consider both the original Gomory–Johnson setting as well as a recent extension by Yıldız and Cornuéjols (Math Oper Res 41:1381–1403, 2016). We show that for any continuous minimal or strongly minimal cut generating function, there exists an extreme cut generating function that approximates the (strongly) minimal function as closely as desired. In other words, the extreme functions are “dense” in the set of continuous (strongly) minimal functions.

Mathematics Subject Classification

90C10 90C57 


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2017

Authors and Affiliations

  • Amitabh Basu
    • 1
  • Robert Hildebrand
    • 2
  • Marco Molinaro
    • 3
  1. 1.Department of Applied Mathematics and StatisticsThe Johns Hopkins UniversityBaltimoreUSA
  2. 2.IBM ResearchYorktown HeightsUSA
  3. 3.Computer Science DepartmentPUC-RIORio de JaneiroBrazil

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