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We study the worst-case convergence rates of the proximal gradient method forminimizing the sum of a smooth strongly convex function and a non-smooth convexfunction whose proximal operator is available.  We establish the exact worst-case convergence rates of the proximal gradientmethod in this setting for any step size and for different standard performancemeasures: objective function accuracy, distance to optimality and residualgradient norm.  The proof methodology relies on recent developments in performance estimationof first-order methods based on semidefinite programming. In the case of theproximal gradient method, this methodology allows obtaining exact andnon-asymptotic worst-case guarantees that are conceptually very simple,although apparently new.  On the way, we discuss how strong convexity can be replaced by weakerassumptions, while preserving the corresponding convergence rates. We alsoestablish that the same fixed step size policy is optimal for all threeperformance measures. Finally, we extend recent results on the worst-casebehavior of gradient descent with exact line search to the proximal case.

Exact worst-case convergence rates of the proximal gradient method for composite convex minimization