  We apply the nonlinear generalized Rayleigh quotients method to develop new
tools, which can be deployed in studying the ground states of the nonlinear
Schr\"{o}dinger (NLS) equations with combined power-type nonlinearities. We
introduce a variational functional, the global minimizer of which corresponds
to the so-called fundamental frequency solutions with prescribed action value.
These solutions, in turn, allow us to find a subset of the physical ground
states, i.e., the ground states of the NLS equation that are preserved under
small perturbations of parameters problem. By this approach, we prove the
orbital stability of the set of physical ground states of the NLS equations in
a generalized sense.
