Answers to: How can I linearize product of a binary and a continuous variables?http://www.or-exchange.com/questions/13120/how-can-i-linearize-product-of-a-binary-and-a-continuous-variables<p>Let X and Y be binary and continuous variables respectively, and there is the product of them in my problem, that is XY. Is there any way to linearize this product in such a way that in the linearized form the binary variable is replaced with a bounded continuous variable?</p>enMon, 21 Dec 2015 17:53:51 -0500Comment by Slavko on Sune's answerhttp://www.or-exchange.com/questions/13120/how-can-i-linearize-product-of-a-binary-and-a-continuous-variables#13145<p>If I omit the binary variable \(X\) I receive a almost linear problem wherein I replace the binary variable product with a continous variable: \(Y = 0\) or \(Y \neq 0\). :-)</p>SlavkoMon, 21 Dec 2015 17:53:51 -0500http://www.or-exchange.com/questions/13120/how-can-i-linearize-product-of-a-binary-and-a-continuous-variables#13145Comment by Paul Rubin on Sune's answerhttp://www.or-exchange.com/questions/13120/how-can-i-linearize-product-of-a-binary-and-a-continuous-variables#13128<p>If you could replace xy with a linear expression involving continuous variables, you would be changing a discontinuous function to a continuous one. I'm pretty sure that would result in the universe imploding spectacularly.</p>Paul RubinFri, 18 Dec 2015 15:53:42 -0500http://www.or-exchange.com/questions/13120/how-can-i-linearize-product-of-a-binary-and-a-continuous-variables#13128Comment by Sune on Sune's answerhttp://www.or-exchange.com/questions/13120/how-can-i-linearize-product-of-a-binary-and-a-continuous-variables#13123<p>If that was indeed possible in the general case, I would expect someone would have suggested that in the other questions.</p>SuneThu, 17 Dec 2015 13:23:34 -0500http://www.or-exchange.com/questions/13120/how-can-i-linearize-product-of-a-binary-and-a-continuous-variables#13123Comment by Amin-Sh on Sune's answerhttp://www.or-exchange.com/questions/13120/how-can-i-linearize-product-of-a-binary-and-a-continuous-variables#13122<p>It is somehow different from those which are asked in the or-exchange. Actually, I want to get rid of binary variable and replace it with a continuous variable.</p>Amin-ShThu, 17 Dec 2015 11:04:15 -0500http://www.or-exchange.com/questions/13120/how-can-i-linearize-product-of-a-binary-and-a-continuous-variables#13122Answer by Sunehttp://www.or-exchange.com/questions/13120/how-can-i-linearize-product-of-a-binary-and-a-continuous-variables/13121<p>I would suggest you to search or-exchange for "linearize". I'm confident you would easily find your answer</p>SuneThu, 17 Dec 2015 10:55:01 -0500http://www.or-exchange.com/questions/13120/how-can-i-linearize-product-of-a-binary-and-a-continuous-variables/13121