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?
My group calls this a "Signomial Equality", and we've implemented a couple useful heuristics for solving this in http://gpkit.rtfd.org; it's also discussed in a 2013 paper by Xu et. al.
My group calls this a "Signomial Equality", and we've implemented a couple useful heuristics for solving this in http://gpkit.rtfd.org; it's also discussed in a 2013 paper by Xu et. al.