Abstract
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 -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 iterations to find either a suitable approximate stationary point of the tensor model or an ε-approximate stationary point of the original objective function.
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