Introduces adaptive strong monotonicity and proves linear convergence of the Generalized Proximal Point Algorithm and stability of its inexact version with bounded, non-vanishing errors.
Inexact Proximal Point and Tseng Algorithms with Nonsummable Errors to Solve Monotone Inclusions
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abstract
In this paper, we establish, for the first time in the literature, the convergence of the practical versions of the Inexact Proximal Point Algorithm (IPPA) and the Inexact Tseng Algorithm (ITA) for computing approximate solutions to monotone inclusions in Hilbert spaces under the the presence of nonsummable errors. Our ap- proach relies on Tikhonov regularization, the contraction property of the associated monotone operators, and the recently developed R-continuity theory. The proposed techniques and results can be extended to analyze various important inexact algorithms in optimization-related problems with nonsummable errors.
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Convergence and Stability Analysis of a Generalized Proximal Point Algorithm and Its Inexact Version
Introduces adaptive strong monotonicity and proves linear convergence of the Generalized Proximal Point Algorithm and stability of its inexact version with bounded, non-vanishing errors.