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Cubic regularization of a Newton scheme and its global performance

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  • NESTEROV, Yurii
  • POLYAK, Boris

Abstract

In this paper we suggest a cubic regularization for a Newton method as applied to unconstrained minimization problem. For this scheme we prove general convergence results. We analyze the behavior of this scheme on different problem classes, for which we get global and local worst-case complexity bounds. It is shown that the search direction can be computed by a standard linear algebra technique.

Suggested Citation

  • NESTEROV, Yurii & POLYAK, Boris, 2003. "Cubic regularization of a Newton scheme and its global performance," LIDAM Discussion Papers CORE 2003041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2003041
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2003.html
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    References listed on IDEAS

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    1. B. T. Polyak, 1998. "Convexity of Quadratic Transformations and Its Use in Control and Optimization," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 553-583, December.
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    Cited by:

    1. Polyak, B.T., 2007. "Newton's method and its use in optimization," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1086-1096, September.
    2. NESTEROV, Yu, 2003. "Modified Gauss-Newton scheme with worst-case guarantees for its global performance," LIDAM Discussion Papers CORE 2003086, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. NESTEROV, Yu., 2006. "Cubic regularization of Newton’s method for convex problems with constraints," LIDAM Discussion Papers CORE 2006039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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