Convex envelopes of products of convex and component-wise concave functions

In this paper, we consider functions of the form f(x,y)=f(x)g(y){phi(x,y)=f(x)g(y)} over a box, where f(x), x ? mathbb R{f(x), xin {mathbb R}} is a nonnegative monotone convex function with a power or an exponential form, and g(y), y ? mathbb Rⁿ{g(y), yin {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.