Preconditioned Nesterov's accelerated gradient descent method and its applications for some nonlinear PDEs
Abstract:
In this talk, we discuss an intuitive understanding of Nesterov’s accelerated gradient descent method, a minimizing scheme that performs better than the gradient descent method, and its convergence result. The treatment is done so that it is suitable for numerical PDEs: the objective functional is required to be only locally Lipschitz smooth rather than globally Lipschitz smooth and the existence of an invariant set is guaranteed. The theory and the intuition are examined by a numerical experiment. Finally, some examples of its application to real-world problems are briefly discussed.