A geometric program, according to Boyd's textbook, is :
$$ \text{minimize } f_0(x)\\ \text{subject to } f_i(x) \leq 1\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, h_i(x) = 1 $$
Where $h_i(x)$ are monomials, and $f_i(x)$ are posynomials.
My question is, if you have a constraint where a posynomial equals one, can you still consider this a geometric program? Or is there some transform that ill turn it back into a geometric program?
Because there exists an equality posynomial constraint, the problem is a signomial program.
I believe the posynomial equality constraint can be approximated by an approximating monomial for $x$ close to some $x_0$.
This would transform the program into a geometric program, which one could solve to update $x_0$. One would then have to re-calculate the monomial approximation of the equality constrained posynomial, and repeat the process until $x_0$ converges.
There is no guarantee for convergence to global minimum in this solution though, so I am open to a more informative answer!