Accelerating the cubic regularization of Newton's method on convex problems

In this paper we propose an accelerated version of the cubic regularization of Newton's method [6]. The original version, used for minimizing a convex function with Lipschitzcontinuous Hessian, guarantees a global rate of convergence of order O( 1 k2 ), where k is the iteration counter. Our modified version converges for the same problem class with order O( 1 k3 ), keeping the complexity of each iteration unchanged. We study the complexity of both schemes on different classes of convex problems. In particular, we argue that for the second-order schemes, the class of non-degenerate problems is different from the standard class.

• Type: Journal
• Year: 2008
• Where: MP
• Authors: Yu. Nesterov
• Keywords: Accelerated Version, Convex Function, Cubic Regularization, MP 2008