Analysis of Krylov subspace solutions of regularized nonconvex quadratic problems

Yair Carmon, John C. Duchi

Research output: Contribution to journalConference articlepeer-review


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/t2 and e4t/p, where 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.

Original languageEnglish
Pages (from-to)10705-10715
Number of pages11
JournalAdvances in Neural Information Processing Systems
StatePublished - 2018
Externally publishedYes
Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: 2 Dec 20188 Dec 2018

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