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Hi Dear Are there anybody that know how to convert this function to linear?

min⁡〖∑(k=1)^K▒∑(i=3)^I▒∑(t=1)^T▒〖(( i * N_it^k )-(i^' * 〖N'〗( i^' t)^k))〗^2 〗

N_it^k and 〖N'〗_( i^' t)^k) are binary variable

asked 13 Nov '16, 02:01

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coolman
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retagged 13 Nov '16, 08:23

Rob%20Pratt's gravatar image

Rob Pratt
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Your formula is a bit mangled, but if I understand correctly, you can linearize as follows. Expand the summand to get an expression of the form \(a x^2 + b y^2 + c x y\), where \(x\) and \(y\) are binary variables. Then replace \(x^2\) and \(y^2\) with \(x\) and \(y\), respectively. Finally, perform the usual linearization of the product of binary variables to replace \(x y\) with binary variable \(z\), yielding \(a x + b y + c z\).

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answered 13 Nov '16, 08:27

Rob%20Pratt's gravatar image

Rob Pratt
1.2k26
accept rate: 28%

edited 14 Nov '16, 00:23

thank you about your answer and excuse me for not clearing of formula, most recently i find this site and i have problem with writing formula.

(13 Nov '16, 23:45) coolman
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Asked: 13 Nov '16, 02:01

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Last updated: 14 Nov '16, 00:23

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