# Seems like geometric programming, except equality constraints

I have an optimization problem, which is quite similar to geometric programming, except that in equality constraints, I have posynomials instead of monomials. Is there any way to change it in to the form of GP?

My idea was to express $p(X)=1$ as $(1-\epsilon)\leq p(X)\leq 1$, and I was so happy that it leads me to an answer, but unfortunately I cannot handle the left-hand side inequality. Any help?