By fractional bilinear constraints, I mean this form:
$$\frac{a_1 + a_2 + a_3 + \cdots}{b_1 + b_2 + b_3 + \cdots} \frac{c_1 + c_2 + c_3 + \cdots}{d_1 + d_2 + d_3 + \cdots}$$
Here, $a,b,c,d$ are variables of the optimization.
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What you've written there is the product of two fractions. What is the constraint exactly? – Oct 07 '14 at 05:17
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That is the constraint. That equal to a constant is the constraint. – sprajagopal Oct 07 '14 at 16:35
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Then it's equivalent to $(a_1+a_2+\cdots)(c_1+c_2+\cdots) = \mathrm{const}\cdot(b_1+b_2+\cdots)(d_1+d_2+\cdots)$, which is a quadratic constraint. – Oct 07 '14 at 17:30
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Alright. That is simply a bilinear constant then. A variation: what if the other side is not a constant but one of the variables? – sprajagopal Oct 08 '14 at 04:06
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What kind of function of the variables is the right hand side? – skr Oct 19 '17 at 05:36
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Perhaps geometric programming can help you. – Richard Dec 28 '21 at 04:42