Goto

Collaborating Authors

 ks tr

Analysis of Krylov Subspace Solutions of Regularized Non-Convex Quadratic Problems

Carmon, Yair, Duchi, John C.

Neural Information Processing Systems

We provide convergence rates for Krylov subspace solutions to the trust-region and cubic-regularized (nonconvex) quadratic problems. Such solutions may be efficiently computed by the Lanczos method and have long been used in practice. We prove error bounds of the form $1/t^2$ and $e^{-4t/\sqrt{\kappa}}$, where $\kappa$ is a condition number for the problem, and $t$ is the Krylov subspace order (number of Lanczos iterations). We also provide lower bounds showing that our analysis is sharp.

  Country:
  Technology:

Add feedback