- On Inexact Solution of Auxiliary Problems in Tensor Methods for Convex Optimization Geovani Grapiglia (grapigliaufpr.br) Yurii Nesterov (yurii.nesterovuclouvain.be) Abstract: In this paper we study the auxiliary problems that appear in p-order tensor methods for unconstrained minimization of convex functions with \nu-Holder continuous pth derivatives. This type of auxiliary problems corresponds to the minimization of a (p+\nu)-order regularization of the pth order Taylor approximation of the objective. For the case p=3, we consider the use of a Gradient Methods with Bregman distance. When the regularization parameter is sufficiently large, we prove that the referred methods take at most O(log(eps^{-1})) iterations to find either a suitable approximate stationary point of the tensor model or an eps-approximate stationary point of the original objective function. Keywords: unconstrained minimization, high-order methods, tensor methods, Holder condition, worst-case global complexity bounds Category 1: Convex and Nonsmooth Optimization Citation: Optimization Methods and Software 36, 145-170 (2021) Download: [PDF]Entry Submitted: 07/30/2019Entry Accepted: 07/30/2019Entry Last Modified: 05/21/2021Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.