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2008

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

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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.
Yu. Nesterov
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where MP
Authors Yu. Nesterov
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