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We focus on the linear convergence of generalized proximal point algorithmsfor solving monotone inclusion problems. Under the assumption that theassociated monotone operator is metrically subregular or that the inverse ofthe monotone operator is Lipschitz continuous, we provide Q-linear and R-linearconvergence results on generalized proximal point algorithms. Comparisonsbetween our results and related ones in the literature are presented in remarksof this work.

Linear Convergence of Generalized Proximal Point Algorithms for Monotone Inclusion Problems