Explicit convex and concave envelopes through polyhedral subdivisions with Unstable Equilibria

Mohit Tawarmalani, Jean-Philippe P. Richard and Chuanhui Xiong

Purdue University Economics Working Papers from Purdue University, Department of Economics

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.

Pages: 36
Date: 2010-06
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Persistent link: https://EconPapers.repec.org/RePEc:pur:prukra:1234

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