  Selecting the fastest algorithm for a specific signal/image processing task
is a challenging question. We propose an approach based on the Performance
Estimation Problem framework that numerically and automatically computes the
worst-case performance of a given optimization method on a class of functions.
We first propose a computer-assisted analysis and comparison of several
first-order primal optimization methods, namely, the gradient method, the
forward-backward, Peaceman-Rachford, and Douglas-Rachford splittings. We
tighten the existing convergence results of these algorithms and extend them to
new classes of functions. Our analysis is then extended and evaluated in the
context of the primal-dual Chambolle-Pock and Condat-V\~u methods.
