Rate of convergence of inertial gradient dynamics with time-dependent viscous damping coefficient
Rate of convergence of inertial gradient dynamics with time-dependent viscous damping coefficient
In a Hilbert space $\mathcal H$ , we study the convergence properties when $t→+∞$ of the trajectories of the second-order differential equation $\begin{equation*}\ddot{x}(t) + γ(t) \dot{x}(t) + \nabla Φ (x(t)) = 0, \;\;\;\;\;\;\;\;{{\rm (IGS)}_{γ}}\end{equation*}$ where $\nablaΦ$ is the gradient of a convex continuously differentiable function $Φ: \mathcal H→\mathbb R$ , …