  In nonlinear electrodynamics, by implementing the causality principle as the
requirement that the group velocity of elementary excitations over a background
field should not exceed the speed of light in the vacuum and the unitarity
principle as the requirement that the residue of the propagator should be
nonnegative, we establish the positive convexity of the effective Lagrangian on
the class of constant fields, also the positivity of all characteristic
dielectric and magnetic permittivity constants that are derivatives of the
effective Lagrangian with respect to the field invariants. Violation of the
general principles by the one-loop approximation in QED at exponentially large
magnetic field is analyzed resulting in complex energy ghosts that signal the
instability of the magnetized vacuum. Superluminal excitations (tachyons)
appear, too, but for the magnetic field exceeding its instability threshold.
Also other popular Lagrangians are tested to establish that the ones leading to
spontaneous vacuum magnetization possess wrong convexity.
