Full power and authority are hereby conferred on every city in this state which now has, or may hereafter have, more than four hundred thousand inhabitants, to provide for and regulate all elections for offices of and under such city and for the nomination of candidates for such offices; and such provision for and regulation of such elections may be effected either by charter provisions therefor adopted by the people of such city according to law, or ordinances therefor duly enacted, or by the people thereof under the power of initiative, if any, reserved in the charter of such city.