What do "signomial equality constraints" mean?
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When I applied gurobi in matlab, it finally told me "gurobi does not support signomial equality constraints".
What kind of constraints are signomial equality constraints? Thank you for reply.
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Hi,
Signomial functions are multivariate polynomials defined as
\[\sum_i c_i \left ( \prod_j x_i^{a_{ij}}\right ) \]
If you want to model a signomial term in Gurobi, you will have to make use of the piecewise-linear approximation function addGenConstrPow and introduce auxiliary variables and equality constraints to model the multilinear part as described in How do I model multilinear terms in Gurobi?
As an example, to model the term \(x\cdot y^{0.4} \cdot z^{1.3} = 0\), you would have to introduce 2 auxiliary variables to model the 2 power terms via the addGenConstrPow function
\[ \begin{align}
w_1 &= y^{0.4}\\
w_2 &= z^{1.3} \end{align}\]
and then add an additional auxiliary variable and equality constraint to model the multilinear term\[ \begin{align}w_3 &= w_1 \cdot w_2\\
x \cdot w_3 &= 0 \end{align} \]Best regards,
Jaromił0 -
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