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We aim at computing the derivative of the solution to a parametricoptimization problem with respect to the involved parameters. For a classbroader than that of strongly convex functions, this can be achieved byautomatic differentiation of iterative minimization algorithms. If theiterative algorithm converges pointwise, then we prove that the derivativesequence also converges pointwise to the derivative of the minimizer withrespect to the parameters. Moreover, we provide convergence rates for bothsequences. In particular, we prove that the accelerated convergence rate of theHeavy-ball method compared to Gradient Descent also accelerates the derivativecomputation. An experiment with L2-Regularized Logistic Regression validatesthe theoretical results.

Automatic Differentiation of Some First-Order Methods in Parametric Optimization