I want to solve an optimization problem for which I have already proven that it is feasible and convex. Introducing further variables and considering a special case of the problem, I can formulate it as geomtric programming problem.
Now I am wondering whether there is any advantage in having a geometric program. In this introduction to geometric programming it is only said that geometric programs are easy to solve, because it is possible to transfer them to convex optimization problems, which in turn can be solved efficiently.
However, considering that I already know that my problem is convex, do I gain anything, if I bring it down to the structure of a geometric program? I yes, how/why?
Depends on your alternative; I'm one of the gpkit developers, and in comparisons we've run GPs solve much faster than naive gradient descent (it's worth noting that not all GPs are convex without the transformation).
However, if your problem is can be solved by another convex solver (e.g. it's also a valid LP) then that solver is likely to be a little bit faster, because GP solvers are not as heavily developed as most other convex solvers.