A frequency-domain analysis of inexact gradient methods

We study robustness properties of some iterative gradient-based methods for strongly convex functions, as well the larger class functions with sector-bounded gradients, under a relative error model. Proofs corresponding convergence rates are based on frequency-domain criteria stability nonlinear systems. Applications given to inexact versions gradient descent and Triple Momentum Method. To further emphasize usefulness methods, we derive improved analytic bounds rate Nesterov’s accelerated method (in exact setting) functions.