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We propose a simple minimization method to show the existence of least energysolutions 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 $(\lambda, u) \in \mathbb{R} \timesH^1 (\mathbb{R}^N)$ is to be determined. The new approach based on the directminimization of the energy functional on the linear combination of Nehari andPohozaev constraints is demonstrated, which allows to provide general growthassumptions imposed on $g$. We cover the most known physical examples andnonlinearities with growth considered in the literature so far as well as weadmit the mass critical growth at $0$.

Normalized ground states of the nonlinear Schr\"{o}dinger equation with at least mass critical growth