Metric Subregularity and the Proximal Point Method
Provides theoretical convergence guarantees for proximal methods in monotone operator theory, relevant to optimization and variational analysis.
The paper proves that metric subregularity is sufficient for linear convergence of the proximal point method for maximal monotone operators, and extends this to randomized and averaged proximal methods for finding common zeros of multiple operators.
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.