CONVERGENCE RATE OF INEXACT PROXIMAL POINT ALGORITHMS FOR OPERATOR WITH HÖLDER METRIC SUBREGULARITY.

We study the issue of strong convergence of inexact proximal point algorithms (introduced by Rockafellar in [SIAM J. Control Optim., 14 (1976), pp. 877-898]) for maximal monotone operators on Hilbert spaces. A unified global/local strong convergence of inexact proximal point algorithms is established under the Hölder metrically subregular condition. Furthermore, quantitative estimates on the convergence rate of inexact proximal point algorithms are also provided. Applying to the special case of the classical (exact) proximal point algorithm, our results improve the corresponding ones in [G. Li and B. S. Mordukhovich, SIAM J. Optim., 22 (2012), pp. 1655-1684]. Finally, as applications, global/local strong convergence and estimates on the convergence rate of inexact proximal point algorithms for optimization problems are presented. [ABSTRACT FROM AUTHOR]