Electro-hydrostatic axes certainly outrun traditional throttle-based solutions in terms of efficiency. However, electromechanical axes set a high standard with their low energy consumption. In order to increase the efficiency of an electro-hydrostatic axis somewhat further to the state of the art, we developed a dynamic optimization algorithm based on dynamic programming to compute a loss optimal displacement trajectory for a given duty cycle. Simulation results show that varying the pump´s displacement and velocity in an optimized way, can achieve an average loss reduction of up to 29 % on all drive train components. The most crucial and complex model in the approach is the one for the radial piston pump which is represented by a trained neural network which respects the actual fluid´s viscosity over a broad range of input values. Five different viscosities are fed into the optimization algorithm and lead to varying optimal displacement trajectories. The developed approach guarantees decent computation time and offers the possibility to make use of high order and non-analytic functions in the loss descriptions. Keywords: loss optimal pump control, dynamic optimization, neural network pump model, speed and displacement variable pump, electro-hydrostatic drive train