We investigate the convergence rates of the trajectories generated byimplicit first and second order dynamical systems associated to thedetermination of the zeros of the sum of a maximally monotone operator and amonotone and Lipschitz continuous one in a real Hilbert space. We show thatthese trajectories strongly converge with exponential rate to a zero of thesum, provided the latter is strongly monotone. We derive from here convergencerates for the trajectories generated by dynamical systems associated to theminimization of the sum of a proper, convex and lower semicontinuous functionwith a smooth convex one provided the objective function fulfills a strongconvexity assumption. In the particular case of minimizing a smooth andstrongly convex function, we prove that its values converge along thetrajectory to its minimum value with exponential rate, too.
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