Quantitative results on a Halpern-type proximal point algorithm

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS（2021）

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Abstract

We apply proof mining methods to analyse a result of Boikanyo and Moroşanu on the strong convergence of a Halpern-type proximal point algorithm. As a consequence, we obtain quantitative versions of this result, providing uniform effective rates of asymptotic regularity and metastability.

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Key words

Proximal point algorithm, Maximally monotone operators, Halpern iteration, Rates of convergence, Rates of metastability, Proof mining

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