How can i linearize this constraint:

$$y = \frac{\text{N}}{x}$$

where N is a constant, x is integer

asked 28 Jan '15, 16:41

zBirdy's gravatar image

zBirdy
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accept rate: 20%

edited 29 Jan '15, 05:44

fbahr's gravatar image

fbahr ♦
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Is \(x\) bounded? If so \((L \le x \le U)\), you replace with it with a sum of binary variables: $$x = \sum_{i=L}^U i x_i$$

Exactly one of the \(x_i\) is nonzero: $$\sum_{i=L}^U x_i = 1$$

Therefore, you can rewrite your constraint as: $$y = \sum_{i=L}^U \frac{N}{i} x_i$$

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answered 28 Jan '15, 17:13

rschwarz's gravatar image

rschwarz
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accept rate: 21%

edited 29 Jan '15, 07:34

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Asked: 28 Jan '15, 16:41

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Last updated: 29 Jan '15, 07:34

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