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Explicit convex and concave envelopes through polyhedral subdivisions |
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| Authors: | Mohit Tawarmalani Jean-Philippe P. Richard Chuanhui Xiong |
| Affiliation: | 1. Krannert School of Management, Purdue University, West Lafayette, IN, USA 2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA 3. School of Business, The University of North Carolina-Pembroke, Pembroke, NC, USA |
| 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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