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On inexact solution of auxiliary problems in tensor methods for convex optimization

Author

Listed:
  • NUNES GRAPIGLIA Geovani,

    (Université catholique de Louvain, Belgium)

  • NESTEROV Yurii,

    (Université catholique de Louvain, CORE, Belgium)

Abstract

In this paper we study the auxiliary problems that appear in p-order tensor methods for unconstrained minimization of convex functions with n-Hölder continuous pth derivatives. This type of auxiliary problems corresponds to the minimization of a (p+n)-order regularization of the pth order Taylor approximation of the objective. For the case p=3, we consider the use of Gradient Methods with Bregman distance. When the regularization parameter is sufficiently large, we prove that the referred methods take at most O(log(e-1)) iterations to find either a suitable approximate stationary point of the tensor model or an e-approximate stationary point of the original objective function.

Suggested Citation

  • NUNES GRAPIGLIA Geovani, & NESTEROV Yurii,, 2019. "On inexact solution of auxiliary problems in tensor methods for convex optimization," LIDAM Discussion Papers CORE 2019030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2019030
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2019.html
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