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Cubic regularization of Newton’s method for convex problems with constraints

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  • NESTEROV, Yu.

Abstract

In this paper we derive effciency estimates of the regularized Newton's method as applied to constrained convex minimization problems and to variational inequalities. We study a one- step Newton's method and its multistep accelerated version, which converges on smooth convex problems as O( 1 k3 ), where k is the iteration counter. We derive also the effciency estimate of a second-order scheme for smooth variational inequalities. Its global rate of convergence is established on the level O( 1 k ).

Suggested Citation

  • 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).
    • Handle: RePEc:cor:louvco:2006039
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2006.html
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    References listed on IDEAS

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    1. NESTEROV, Yu, 2003. "Dual extrapolation and its applications for solving variational inequalities and related problems," LIDAM Discussion Papers CORE 2003068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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).
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    Cited by:

    1. Hande Benson & David Shanno, 2014. "Interior-point methods for nonconvex nonlinear programming: cubic regularization," Computational Optimization and Applications, Springer, vol. 58(2), pages 323-346, June.

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