Is it possible to determine if a Geometric Program (GP) has one, none, or infinite (primal) solutions by its structure (e.g., in terms of the number of variables, constraints, or product terms involved in the problem)?
It is known that the "degree of difficulty" (see e.g. this def.) determines the number of solutions to the dual problem, but how that relates to the number of primal solutions?
I am interested in proving that a GP has a unique solution, i.e. when the set of optimal solutions is a singleton.