  In this paper, we introduce two minimization problems on non-scattering
solutions to nonlinear Schr\"odinger equation. One gives us a sharp scattering
criterion, the other is concerned with minimal size of blowup profiles. We
first reformulate several previous results in terms of these two minimizations.
Then, the main result of the paper is existence of minimizers to the both
minimization problems for mass-subcritical nonlinear Schr\"odinger equations.
To consider the latter minimization, we consider the equation in a Fourier
transform of generalized Morrey space. It turns out that the minimizer to the
latter problem possesses a compactness property, which is so-called almost
periodicity modulo symmetry.
