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

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  • NESTEROV, Yu.

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.

Suggested Citation

  • NESTEROV, Yu., 2005. "Accelerating the cubic regularization of Newton’s method on convex problems," LIDAM Discussion Papers CORE 2005068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2005068
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