On inexact solution of auxiliary problems in tensor methods for convex optimization
(2021) Optimization Methods and Software — Vol. 36, n° 1, p. 145-170 (2021)
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- Authors
Nesterov, Yurii 
- 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 pth derivatives. This type of auxiliary problems corresponds to the minimization of a (p + ν)-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 ${\Os(log(\epsilon^{-1}))$ iterations to find either a suitable approximate stationary point of the tensor model or an $\epsilon$-approximate stationary point of the original objective function.
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Citations
Nunes Grapiglia, G., & Nesterov, Y. (2021). On inexact solution of auxiliary problems in tensor methods for convex optimization. Optimization Methods and Software, 36(1), 145-170. https://doi.org/10.1080/10556788.2020.1731749 (Original work published 2021)