Error estimates for iterative algorithms for minimizing regularized quadratic subproblems

Published: 2019/03/30, Updated: 2019/04/01

Nonlinear Optimization cubic regularization subproblem, error estimates, krylov methods, trust-region methods Short URL: https://optimization-online.org/?p=15736

We derive bounds for the objective errors and gradient residuals when finding approximations to the solution of common regularized quadratic optimization problems within evolving Krylov spaces. These provide upper bounds on the number of iterations required to achieve a given stated accuracy. We illustrate the quality of our bounds on given test examples.

Citation

Technical Report RAL-TR-2019-004, STFC-Rutherford Appleton Laboratory, Oxfordshire, England, March 2019

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