A frequency-domain analysis of inexact gradient descent

12/31/2019

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by   Oran Gannot, et al.

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We study robustness properties of inexact gradient descent for strongly convex functions, as well as for the larger class of functions with sector-bounded gradients, under a relative error model. Proofs of the corresponding convergence rates are based on frequency-domain criteria for the stability of nonlinear systems perturbed by additive noise.