Abstract
In this paper, we consider functions of the form \({\phi(x,y)=f(x)g(y)}\) over a box, where \({f(x), x\in {\mathbb R}}\) is a nonnegative monotone convex function with a power or an exponential form, and \({g(y), y\in {\mathbb R}^n}\) is a component-wise concave function which changes sign over the vertices of its domain. We derive closed-form expressions for convex envelopes of various functions in this category. We demonstrate via numerical examples that the proposed envelopes are significantly tighter than popular factorable programming relaxations.
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This research was supported in part by National Science Foundation award CMII-1030168.
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Khajavirad, A., Sahinidis, N.V. Convex envelopes of products of convex and component-wise concave functions. J Glob Optim 52, 391–409 (2012). https://doi.org/10.1007/s10898-011-9747-5
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DOI: https://doi.org/10.1007/s10898-011-9747-5