Quantitative results for a Tseng-type primal-dual method for composite monotone inclusions

Ulrich Kohlenbach; Nicholas Pischke

doi:10.1007/s10589-025-00744-2

Quantitative results for a Tseng-type primal-dual method for composite monotone inclusions

Ulrich Kohlenbach
, Nicholas Pischke

Technische Universität Darmstadt

Research output: Contribution to journal › Article › peer-review

Abstract

We provide quantitative results on a seminal Tseng-type primal-dual splitting algorithm for solving monotone inclusions due to Combettes and Pesquet which involves a mixture of sums, linear compositions and parallel sums of set-valued and Lipschitzian operators. For that, we first give quantitative results on a version of Tseng’s forward-backward-forward splitting algorithm including error terms and variable parameters, partially extending previous work of Treusch and Kohlenbach, to which the method of Combettes and Pesquet is then reduced.

Original language	English
Pages (from-to)	1191-1223
Number of pages	33
Journal	Computational Optimization and Applications
Volume	93
Issue number	3
Early online date	13 Dec 2025
DOIs	https://doi.org/10.1007/s10589-025-00744-2
Publication status	Published - 30 Apr 2026

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

Acknowledgements

We want to thank Radu Ioan Boţ for suggesting the work [4] as an interesting case
study for proof mining in the context of splitting methods.

Funding

Open Access funding enabled and organized by Projekt DEAL

Keywords

Splitting algorithms
Tseng’s algorithm
Monotone inclusions
Rates of convergence
Rates of metastability
Proof mining

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10.1007/s10589-025-00744-2Licence: CC BY

Cite this

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abstract = "We provide quantitative results on a seminal Tseng-type primal-dual splitting algorithm for solving monotone inclusions due to Combettes and Pesquet which involves a mixture of sums, linear compositions and parallel sums of set-valued and Lipschitzian operators. For that, we first give quantitative results on a version of Tseng{\textquoteright}s forward-backward-forward splitting algorithm including error terms and variable parameters, partially extending previous work of Treusch and Kohlenbach, to which the method of Combettes and Pesquet is then reduced.",

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N2 - We provide quantitative results on a seminal Tseng-type primal-dual splitting algorithm for solving monotone inclusions due to Combettes and Pesquet which involves a mixture of sums, linear compositions and parallel sums of set-valued and Lipschitzian operators. For that, we first give quantitative results on a version of Tseng’s forward-backward-forward splitting algorithm including error terms and variable parameters, partially extending previous work of Treusch and Kohlenbach, to which the method of Combettes and Pesquet is then reduced.

AB - We provide quantitative results on a seminal Tseng-type primal-dual splitting algorithm for solving monotone inclusions due to Combettes and Pesquet which involves a mixture of sums, linear compositions and parallel sums of set-valued and Lipschitzian operators. For that, we first give quantitative results on a version of Tseng’s forward-backward-forward splitting algorithm including error terms and variable parameters, partially extending previous work of Treusch and Kohlenbach, to which the method of Combettes and Pesquet is then reduced.

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KW - Tseng’s algorithm

KW - Monotone inclusions

KW - Rates of convergence

KW - Rates of metastability

KW - Proof mining

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JF - Computational Optimization and Applications

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ER -

Quantitative results for a Tseng-type primal-dual method for composite monotone inclusions

Abstract

Bibliographical note

Acknowledgements

Funding

Keywords

Access to Document

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