Optimal Combination of Tensor Optimization Methods

@inproceedings{Kamzolov2020OptimalCO,
  title={Optimal Combination of Tensor Optimization Methods},
  author={D. Kamzolov and A. Gasnikov and P. Dvurechensky},
  booktitle={OPTIMA},
  year={2020}
}
We consider the minimization problem of a sum of a number of functions having Lipshitz $p$-th order derivatives with different Lipschitz constants. In this case, to accelerate optimization, we propose a general framework allowing to obtain near-optimal oracle complexity for each function in the sum separately, meaning, in particular, that the oracle for a function with lower Lipschitz constant is called a smaller number of times. As a building block, we extend the current theory of tensor… Expand
Affine-invariant contracting-point methods for Convex Optimization
Inexact Tensor Methods and Their Application to Stochastic Convex Optimization
On the Computational Efficiency of Catalyst Accelerated Coordinate Descent
Accelerated meta-algorithm for convex optimization
Near-Optimal Hyperfast Second-Order Method for convex optimization and its Sliding.
Oracle Complexity Separation in Convex Optimization

References

SHOWING 1-10 OF 34 REFERENCES
On inexact solution of auxiliary problems in tensor methods for convex optimization
Implementable tensor methods in unconstrained convex optimization
  • Y. Nesterov
  • Mathematics, Computer Science
  • Math. Program.
  • 2021
An Optimal High-Order Tensor Method for Convex Optimization
Optimal Tensor Methods in Smooth Convex and Uniformly ConvexOptimization
Gradient methods for minimizing composite functions
  • Y. Nesterov
  • Mathematics, Computer Science
  • Math. Program.
  • 2013
Oracle complexity of second-order methods for smooth convex optimization
Local convergence of tensor methods
...
1
2
3
4
...