  We aim at computing the derivative of the solution to a parametric
optimization problem with respect to the involved parameters. For a class
broader than that of strongly convex functions, this can be achieved by
automatic differentiation of iterative minimization algorithms. If the
iterative algorithm converges pointwise, then we prove that the derivative
sequence also converges pointwise to the derivative of the minimizer with
respect to the parameters. Moreover, we provide convergence rates for both
sequences. In particular, we prove that the accelerated convergence rate of the
Heavy-ball method compared to Gradient Descent also accelerates the derivative
computation. An experiment with L2-Regularized Logistic Regression validates
the theoretical results.
