On linearization of the product of two continuous variables

Linearization of nonlinear functions is a common strategy that researchers use in many practical optimization problems due to existence of more powerful linear programming algorithms. In this note, an approximate technique for linearizing the polynomial term obtained by multiplying two continuous variables is studied. A constructive demonstration of the linearization technique is presented in detail which helps to show that the previously claimed upper bound on its error of approximation is incorrect and may therefore lead to solutions that are not accurate enough. Furthermore, to prevent misuse of the mentioned technique, we determine the best upper bound on its error of approximation.