Piecewise linear approximation of functions of two variables in MILP models

In recent years, the increased efficiency of mixed integer linear programming (MILP) software tools has encouraged their use also in the solution of non-linear problems, bringing to the need for efficient techniques to linearize non-linear functions of one or more variables. The standard methodologies consist in the piecewise linear approximation of such functions. We consider three easy-to-implement methods for the piecewise linear approximation of functions of two variables. We experimentally evaluate their approximation quality, and give a detailed description of how the methods can be embedded in a MILP model. The advantages and drawbacks of the three methods are discussed on numerical examples.