Before revision: We analyze preconditioned Nesterov's accelerated gradient descent methods (PAGD) for approximating the minimizer of locally Lipschitz smooth, strongly convex objective functionals.
After revision: We analyze preconditioned Nesterov's accelerated gradient descent method (AGD) to the approximation of solutions of a wide class of partial differential equations (PDEs). This is achieved by proving the existence of an invariant set and exponential convergence rates when its preconditioned version (PAGD) is applied to minimize locally Lipschitz smooth, strongly convex objective functionals.