A Convex Envelope Formula for Multilinear Functions
Journal of Global Optimization
Semidefinite Relaxations of Fractional Programs via Novel Convexification Techniques
Journal of Global Optimization
MINLPLib--A Collection of Test Models for Mixed-Integer Nonlinear Programming
INFORMS Journal on Computing
Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave Envelopes
Journal of Global Optimization
Convex envelopes for edge-concave functions
Mathematical Programming: Series A and B
Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
The Convex Envelope of ($n$-1)-Convex Functions
SIAM Journal on Optimization
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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.