Year: 2020
Type: article
Abstract: In this paper we study the auxiliary problems that appear in $p$-order tensor methods for unconstrained minimization of convex functions with $ν$-Hölder continuous $p$th derivatives. This type of auxiliary problems corresponds to the minimization of a $(p+ν)$-order regularization of the $p$th 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 $\mathcal{O}(\log(ε^{-1}))$ iterations to find either a suitable approximate stationary point of the tensor model or an $ε$-approximate stationary point of the original objective function.
Source: Optimization methods & software
Authors: G.N. Grapiglia, Yu. Nesterov
Institutions: Universidade Federal do Paraná, UCLouvain
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Awards: G3774921934, G7634775220
OpenAlex ID: W2966628707