Attractive properties of subgradient methods, such as robust stability and linear convergence, has been emphasized when they are used to solve nonsmooth optimization problems with sharp minima [12, 13]. In this letter we extend the robustness results to the composite convex models and show that the basic proximal gradient algorithm under the presence of a sufficiently low noise still converges in finite time, even if the noise is persistent.
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View Finite convergence of the inexact proximal gradient method to sharp minima