Tensor Methods for Minimizing Convex Functions with Hölder Continuous Higher-Order Derivatives

  title={Tensor Methods for Minimizing Convex Functions with H{\"o}lder Continuous Higher-Order Derivatives},
  author={G. N. Grapiglia and Y. Nesterov},
  journal={SIAM J. Optim.},
In this paper we study p-order methods for unconstrained minimization of convex functions that are p-times differentiable (p ≥ 2) with n-Holder continuous p th derivatives. We propose tensor schemes with and without acceleration. For the schemes without acceleration, we establish iteration complexity bounds of O(e-1/(p+n-1))$ for reducing the functional residual below a given e I\in (0,1). Assuming that n is known, we obtain an improved complexity bound of O(e-1/(p+n))$ for the corresponding… Expand
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