I am solving a convex optimization problem in python cvxopt.
I know I can add the lower bound and upper bound using Gx <= h constraint. However, this increases the dimensionality of the problem. In addition to that in scenarios during solution process, my decision variable becomes negative.
Given the available APIs of all cvxopt-based solvers, there is no way for this but using constraints as you described. Keep in mind, that given those solvers, there is no explicit handling of bounds in the underlying theory of conic optimizers (Interior-point methods only). Also: those constraints are very sparse and dimensionality is a negligible factor compared to sparsity-ratios / patterns.
This is of course different for Simplex-type solvers (explicit treatment of bounds). But for external solvers like GLPK/MOSEK this is also not supported.
(I don't get your last point. Maybe make it more clear!)
