Mathematical Programming

, Volume 138, Issue 1–2, pp 531–577 | Cite as

Explicit convex and concave envelopes through polyhedral subdivisions

  • Mohit Tawarmalani
  • Jean-Philippe P. Richard
  • Chuanhui Xiong
Full Length Paper Series A


In this paper, we derive explicit characterizations of convex and concave envelopes of several nonlinear functions over various subsets of a hyper-rectangle. These envelopes are obtained by identifying polyhedral subdivisions of the hyper-rectangle over which the envelopes can be constructed easily. In particular, we use these techniques to derive, in closed-form, the concave envelopes of concave-extendable supermodular functions and the convex envelopes of disjunctive convex functions.

Mathematics Subject Classification

47N10 90C26 52A27 90C11 


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Copyright information

© Springer and Mathematical Optimization Society 2012

Authors and Affiliations

  • Mohit Tawarmalani
    • 1
  • Jean-Philippe P. Richard
    • 2
  • Chuanhui Xiong
    • 1
    • 3
  1. 1.Krannert School of ManagementPurdue UniversityWest LafayetteUSA
  2. 2.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.School of BusinessThe University of North Carolina-PembrokePembrokeUSA

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