Explicit convex and concave envelopes through polyhedral subdivisions with Unstable Equilibria
AbstractIn 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 InfoPaper provided by Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1234.
Date of creation: Jun 2010
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-09-03 (All new papers)
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- 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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