Dear All,
I have the following question.
Suppose we have a system of ODEs dx/dt=f(x) for which V(x) is a Lyapunov function, i.e. dV/dt < 0 and V>=0 with V(x^*)=0, where x^* is a fixed (or equilibrium) point of ODE.
If V(x) is also a convex function of x then the gradient descent equation dx/dt=-dV/dx will gives us a "lower bound on time it takes to converge to equilibrium" for any ODE, i.e. any f(x).