Analysis of Krylov Subspace Solutions of Regularized Nonconvex Quadratic Problems
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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 haveplong been used in practice. We prove error bounds of the form 
and 
where k 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.
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