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

GRAPIGLIA Geovani, Nunes () and Yurii, Nesterov ()
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GRAPIGLIA Geovani, Nunes: Université catholique de Louvain, Belgium
Yurii, Nesterov: Université catholique de Louvain, CORE, Belgium

No 2019030, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Keywords: unconstrained minimization; high-order methods; tensor methods; Hölder condition; worst-case global complexity bounds (search for similar items in EconPapers)
Date: 2019-12-17
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2019030

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