In this paper, we generalize (accelerated) Newton's method with cubic regularization under inexact second-order information for (strongly) convex optimization problems. Under mild assumptions, we provide global rate of convergence of these methods and show the explicit dependence of the rate of convergence on the problem parameters. While the complexity bounds of our presented algorithms are theoretically worse than those of their exact counterparts, they are at least as good as those of the optimal first-order methods. Our numerical experiments also show that using inexact Hessians can significantly speed up the algorithms in practice. keywords convex optimization, strongly convex problems, inexact Newton method, Hessian approximation, accelerated methods.
Recently, REF proposed an accelerated Newton's method with cubic regularization using inexact second-order information.
Second-Order Methods with Cubic Regularization Under Inexact Information
arXiv: Optimization and Control
Mathematics