Glovers linearization

Given a binary variable $LaTeX: x$ and a linear function $LaTeX: f(w)$ in discrete and/or continuous variables $LaTeX: w$ in $LaTeX: W$ for some set $LaTeX: W$, this linearization reformulates the product $LaTeX: f(w)x$ with a (free) continuous variable $LaTeX: z$ and enforces that $LaTeX: z = f(w)x$ by adding four linear inequalities:

$LaTeX: Lx \le z \le Ux, \; f(w) - U(1-x) \le z \le f(w) - L(1-x),$

where the values $LaTeX: L$ and $LaTeX: U$ are defined as

$LaTeX: L = \min \{ f(w) : w \in W^R\} \mbox{ and } U = \max \{f(w) : w \in W^R\},$

and $LaTeX: W^R$ is any relaxation of $LaTeX: W$.