From inertial systems to proximal flows

par Kouegnon Denis MITCHOZOUNNOU

vendredi 14 nov. 2025, 10:30 → 11:00 Europe/Paris

XR203 (XLIM)

We study the asymptotic behavior of trajectories of a class of second-order dynamical systems involving an implicit Hessian-driven damping term, governed by a parameter α > 0. These second-order dynamics can be viewed as continuous counterparts to accelerated gradient methods such as Nesterov and Ravine, and arise naturally in the regularization of Newton-type schemes. They can also be interpreted as time-rescaled inertial dynamics with memory effects. We analyze the limit as α → +∞, and prove that the trajectories converge, uniformly on compact intervals, to the solution of a first-order differential equation of the form y'(s) + ∇f ( y(s) + β0 y'(s)) = 0.