Local convergence of tensor methods

Understand

In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective.

• We justify local superlinear convergence under the assumption of uniform convexity of the smooth component, having Lipschitz-continuous high-order derivative.
• The convergence both in function value and in the norm of minimal subgradient is established.
• Global complexity bounds for the Composite Tensor Method in convex and uniformly convex cases are also discussed.