  Motivated by the fact that both the classical and quantum description of
nature rest on causality and a variational principle, we develop a novel and
highly versatile discretization prescription for classical initial value
problems (IVPs). It is based on an optimization (action) functional with
doubled degrees of freedom, which is discretized using a single regularized
summation-by-parts (SBP) operator. Formulated as optimization task it allows us
to obtain classical trajectories without the need to derive an equation of
motion. The novel regularization we develop in this context is inspired by the
weak imposition of initial data, often deployed in the modern treatment of IVPs
and is implemented using affine coordinates. We demonstrate numerically the
stability, accuracy and convergence properties of our approach in systems with
classical equations of motion featuring both first and second order derivatives
in time. onvergence properties of our approach in systems with classical
equations of motion featuring both first and second order derivatives in time.
