Convergence rates of damped inerial dynamics from multi-degree-of-freedom system

In this article, we investigate the convergence rate of the following dynamic system in R-n (x) over dot (t) + A/t(theta)(x) over dot(t) + del F(x(t)) = 0, t > 0, where A denotes the constant positive definite matrix and the potential function F : R-n -> R is continuous differentiable. This system is of vital importance, especially in optimization and engineering. This article presents new convergence rates of the above dynamics when F(x) satisfies some local geometrical properties by constructing a proper Lyapunov function. Finally, some numerical experiments were performed to explain the convergence results.