Analysis of Krylov subspace solutions of regularized nonconvex quadratic problems

Yair Carmon; John C. Duchi

Analysis of Krylov subspace solutions of regularized nonconvex quadratic problems

Research output: Contribution to journal › Conference article › peer-review

Abstract

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 language	English
Pages (from-to)	10705-10715
Number of pages	11
Journal	Advances in Neural Information Processing Systems
Volume	2018-December
State	Published - 2018
Externally published	Yes
Event	32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada Duration: 2 Dec 2018 → 8 Dec 2018

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Information Systems
Signal Processing

Cite this

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title = "Analysis of Krylov subspace solutions of regularized nonconvex quadratic problems",

abstract = "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.",

author = "Yair Carmon and Duchi, {John C.}",

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year = "2018",

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T1 - Analysis of Krylov subspace solutions of regularized nonconvex quadratic problems

AU - Carmon, Yair

AU - Duchi, John C.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85064820706&partnerID=8YFLogxK

M3 - مقالة من مؤنمر

SN - 1049-5258

VL - 2018-December

SP - 10705

EP - 10715

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

T2 - 32nd Conference on Neural Information Processing Systems, NeurIPS 2018

Y2 - 2 December 2018 through 8 December 2018

ER -

Analysis of Krylov subspace solutions of regularized nonconvex quadratic problems

Abstract

All Science Journal Classification (ASJC) codes

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