I had a question about reformulating a signomial constraint into a standard GP one. Here is a constraint with a quotient of two signomials,
$\frac{A(\mathbf{P})}{ B(\mathbf{P})} \leq t$
where $t>0$ is a slack variable. I planned to reformulate it into a standard GP one (such as a form of posynomial/monomial).
My first step is to separate the positive and negative terms in both numerator and denominator as
$\frac{A(\mathbf{P})^{+}-A(\mathbf{P})^{-}}{ B(\mathbf{P})^{+}-B(\mathbf{P})^{-}} \leq t~~~(2)$
where $B(\mathbf{P})^{+}-B(\mathbf{P})^{-}>0$. The second step is to multiply the denominator by t, and reformulate (2) as follows
$\frac{A(\mathbf{P})^{+}+tB(\mathbf{P})^{-}}{ A(\mathbf{P})^{-}+tB(\mathbf{P})^{+}} \leq 1$
Here, the original constraint became a quotient of two posynomials, and then the posynomial denominator can be approximated to a monomial one, which finally became a standard GP. I am not sure if this tranformation is correct or not, since I often get NAN by using CVX.