We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal monotone operator. This result is then generalized to obtain convergence rates for the problem of finding a common zero of multiple monotone operators by considering randomized and averaged proximal methods.
A bundle method using two polyhedral approximations of the epsilon-enlargement of a maximal monotone operator
Local Convergence of the Proximal Point Method for a Special Class of Nonconvex Functions on Hadamard Manifolds
From Proximal Point Method to Nesterov's Acceleration
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