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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
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    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.

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    Bibliographic Info

    Paper provided by Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1234.

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    Length: 36
    Date of creation: Jun 2010
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    Handle: RePEc:pur:prukra:1234

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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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