  Periodic waves are standing wave solutions of nonlinear Schr\''odinger
equations whose profile is periodic in space dimension one. We consider general
nonlinearities and provide variational characterizations for the periodic wave
profiles. This involves minimizing energy while keeping mass and momentum
constant, as well as minimizing the action over the Nehari manifold. These
variational approaches are considered both in the periodic and anti-periodic
settings, and for focusing and defocusing nonlinearities. In appendix, we study
the existence properties of periodic solutions of the triple power
nonlinearity.
