  We propose a simple minimization method to show the existence of least energy
solutions to the normalized problem \begin{cases}
  -\Delta u + \lambda u = g(u) \quad \mathrm{in} \ \mathbb{R}^N, \ N \geq 3, \\
u \in H^1(\mathbb{R}^N), \\ \int_{\mathbb{R}^N} |u|^2 \, dx = \rho > 0,
\end{cases} where $\rho$ is prescribed and $(\lambda, u) \in \mathbb{R} \times
H^1 (\mathbb{R}^N)$ is to be determined. The new approach based on the direct
minimization of the energy functional on the linear combination of Nehari and
Pohozaev constraints is demonstrated, which allows to provide general growth
assumptions imposed on $g$. We cover the most known physical examples and
nonlinearities with growth considered in the literature so far as well as we
admit the mass critical growth at $0$.
