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?

asked 17 Dec '15, 08:44

Amin-Sh's gravatar image

Amin-Sh
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I would suggest you to search or-exchange for "linearize". I'm confident you would easily find your answer

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answered 17 Dec '15, 10:55

Sune's gravatar image

Sune
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accept rate: 20%

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.

(17 Dec '15, 11:04) Amin-Sh

If that was indeed possible in the general case, I would expect someone would have suggested that in the other questions.

(17 Dec '15, 13:23) Sune
2

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.

(18 Dec '15, 15:53) Paul Rubin ♦♦

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 \(Y \neq 0\). :-)

(21 Dec '15, 17:53) Slavko
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Asked: 17 Dec '15, 08:44

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Last updated: 21 Dec '15, 17:56

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