This paper investigates optimal control for a large population of identical plug-in electric vehicles (PEVs). A mean field assumption is formulated to describe the evolution of the PEVs population and its interaction with the central planner, leading to partial differential equations (PDE). The optimization problem is formulated in the setting of discrete time and state spaces and is convex, but not necessarily linear or quadratic. Two constraints on the population of electric vehicles (EVs) are concerned: a minimal state of charge (SoC) per EV at the end of the charging period and an aggregate power demand constraint. The Chambolle-Pock algorithm is applied to obtain a numerical solution. We study, in two numerical examples, different cost functions that avoid charging synchronization among the EV population.