Glovers linearization

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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.


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