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

Yu. Nesterov

No 2005068, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: 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 Lipschitz-continuous Hessian, guarantees a global rate of convergence of order O(1/k exp.2), where k is the iteration counter. Our modified version converges for the same problem class with order O(1/k exp.3), 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.

Keywords: convex optimization; unconstrained minimization; Newton’s method; cubic regularization; worst-case complexity; global complexity bounds; non-degenerate problems; condition number (search for similar items in EconPapers)
Date: 2005-10
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