  Viewing optimization methods as numerical integrators for ordinary
differential equations (ODEs) provides a thought-provoking modern framework for
studying accelerated first-order optimizers. In this literature, acceleration
is often supposed to be linked to the quality of the integrator (accuracy,
energy preservation, symplecticity). In this work, we propose a novel ordinary
differential equation that questions this connection: both the explicit and the
semi-implicit (a.k.a symplectic) Euler discretizations on this ODE lead to an
accelerated algorithm for convex programming. Although semi-implicit methods
are well-known in numerical analysis to enjoy many desirable features for the
integration of physical systems, our findings show that these properties do not
necessarily relate to acceleration.
