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Quantitative results on a Halpern-type proximal point algorithm

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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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Acknowledgements

Laurenţiu Leuştean was partially supported by a grant of the Romanian Ministry of Research and Innovation, Program 1 - Development of the National RDI System, Subprogram 1.2 - Institutional Performance - Projects for Funding the Excellence in RDI, Contract Number 15PFE/2018. Pedro Pinto acknowledges and is thankful for the financial support of: FCT - Fundação para a Ciência e a Tecnologia under the Project UID/MAT/04561/2019; the research center Centro de Matemática, Aplicações Fundamentais com Investigação Operacional, Universidade de Lisboa; and the ‘Future Talents’ short-term scholarship at Technische Universität Darmstadt. The paper also benefited from discussions with Fernando Ferreira and Ulrich Kohlenbach.

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Authors and Affiliations

  1. Research Center for Logic, Optimization and Security (LOS), Department of Computer Science, Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014, Bucharest, Romania

    Laurenţiu Leuştean

  2. Simion Stoilow Institute of Mathematics of the Romanian Academy, Calea Griviţei 21, 010702, Bucharest, Romania

    Laurenţiu Leuştean

  3. Department of Mathematics, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289, Darmstadt, Germany

    Pedro Pinto

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  1. Laurenţiu Leuştean
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  2. Pedro Pinto
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Correspondence to Laurenţiu Leuştean.

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Leuştean, L., Pinto, P. Quantitative results on a Halpern-type proximal point algorithm. Comput Optim Appl 79, 101–125 (2021). https://doi.org/10.1007/s10589-021-00263-w

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