Tensor Methods for Minimizing Convex Functions with Hölder Continuous Higher-Order Derivatives
In this paper we study p-order methods for unconstrained minimization of convex functions that are p-times differentiable with $\nu$-Hölder continuous pth derivatives. We propose tensor schemes with and without acceleration. For the schemes without acceleration, we establish iteration complexity bounds of $\mathcal{O}\left(\epsilon^{-1/(p+\nu-1)}\right)$ for reducing the functional residual below a given $\epsilon\in (0,1)$. Assuming that $\nu$ … Read more