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Accelerated regularized Newton methods for minimizing composite convex functions

Author

Listed:
  • GRAPIGLIA Geovani,

    (Universidade Federal do Parana, Brazil)

  • NESTEROV Yurii,

    (CORE, Université catholique de Louvain)

Abstract

In this paper, we study accelerated Regularized Newton Methods for minimizing objectives formed as a sum of two functions: one is convex and twice differentiable with Hölder-continuous Hessian, and the other is a simple closed convex function. For the case in which the Hölder parameter $\nu \in [0,1]$ is known, we propose methods that make at most $\cal {O}\left(\frac {1} {\epsilon^{1/(2+\nu)}}\right)$ iterations to reduce the funcitonal residual below a given precision $\epsilon > 0$. For the general case, in which the $\nu$ is not known, we proposeo a universal method that ensures the same precision in at most $\cal{O} \left(\frac {1} {\epsilon^{2/[3(1+\nu)]}}\right)$ iterations.

Suggested Citation

  • GRAPIGLIA Geovani, & NESTEROV Yurii,, 2018. "Accelerated regularized Newton methods for minimizing composite convex functions," LIDAM Discussion Papers CORE 2018010, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2018010
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2018.html
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