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Explicit convex and concave envelopes through polyhedral subdivisions with Unstable Equilibria

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  • Mohit Tawarmalani
  • Jean-Philippe P. Richard
  • Chuanhui Xiong

Abstract

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.

Suggested Citation

  • Mohit Tawarmalani & Jean-Philippe P. Richard & Chuanhui Xiong, 2010. "Explicit convex and concave envelopes through polyhedral subdivisions with Unstable Equilibria," Purdue University Economics Working Papers 1234, Purdue University, Department of Economics.
  • Handle: RePEc:pur:prukra:1234
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    File URL: http://www.krannert.purdue.edu/programs/phd/Working-papers-series/2010/1234.pdf
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    Cited by:

    1. Keith Zorn & Nikolaos Sahinidis, 2014. "Global optimization of general nonconvex problems with intermediate polynomial substructures," Journal of Global Optimization, Springer, vol. 59(2), pages 673-693, July.

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