  Geometric numerical integration has recently been exploited to design
symplectic accelerated optimization algorithms by simulating the Lagrangian and
Hamiltonian systems from the variational framework introduced in Wibisono et
al. In this paper, we discuss practical considerations which can significantly
boost the computational performance of these optimization algorithms, and
considerably simplify the tuning process. In particular, we investigate how
momentum restarting schemes ameliorate computational efficiency and robustness
by reducing the undesirable effect of oscillations, and ease the tuning process
by making time-adaptivity superfluous. We also discuss how temporal looping
helps avoiding instability issues caused by numerical precision, without
harming the computational efficiency of the algorithms. Finally, we compare the
efficiency and robustness of different geometric integration techniques, and
study the effects of the different parameters in the algorithms to inform and
simplify tuning in practice. From this paper emerge symplectic accelerated
optimization algorithms whose computational efficiency, stability and
robustness have been improved, and which are now much simpler to use and tune
for practical applications.
