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PreprintCC BY 4.0arXiv

Inexact Proximal Point and Tseng Algorithms with Nonsummable Errors to Solve Monotone Inclusions

  • Ba Khiet Le
  • Boris S. Mordukhovich
  • Michel A. Thera
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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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Cite

BibTeXRIS
BibTeX
@misc{le2026inexact,
  title = {{Inexact Proximal Point and Tseng Algorithms with Nonsummable Errors to Solve Monotone Inclusions}},
  author = {Ba Khiet Le and Boris S. Mordukhovich and Michel A. Thera},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.01536},
  eprint = {2606.01536},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.01536},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Inexact Proximal Point and Tseng Algorithms with Nonsummable Errors to Solve Monotone Inclusions
AU  - Ba Khiet Le
AU  - Boris S. Mordukhovich
AU  - Michel A. Thera
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2606.01536
UR  - https://arxiv.org/abs/2606.01536
AB  - 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.
ER  -