This paper proposes a parallelized online optimization of low voltage distribution network (LVDN) operation. It is performed on a graphics processing unit (GPU) by combining the optimization procedure with the load flow method. In the case study, performed for the test LVDN with distributed generators (DGs) and controllable loads, differential evolution optimization based on a backward-forward sweep load flow method was parallelized on GPU. The goal of online optimization is to keep the LVDN voltage profile within the prescribed limits, to minimize LVDN losses, and to enable demand response functionality. This is achieved by the optimization determined reference values for the controllable load's operation, and the reactive power generation, and active power curtailment of DGs. The results show that the parallelized GPU implemented optimization can be significantly faster than similar implementation on a central processing unit, and is, therefore, suitable for the online optimization of the presented LVDN.