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PreprintCC BY 4.0arXiv

Reducing the Lipschitz Constant in Tseng Algorithm and the Convergence Analysis

  • Ba Khiet Le
  • Minh Thuan Tran
  • Thi Thanh Tien Pham
  • Kim Thuong Vo
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Abstract

In this paper, we prove the weak and linear convergence of Tseng algorithm applied to the zero of sum of two operators problem where each operator is not necessarily monotone while existing researches in the literature require the monotonicity of both operators. Consequently it allows us to decompose more efficiently and can reduce the Lipschitz constant significantly, which is meaningful especially in big data. Numerical examples supporting the theoretical results are also provided.

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Cite

BibTeXRIS
BibTeX
@misc{le2026reducing,
  title = {{Reducing the Lipschitz Constant in Tseng Algorithm and the Convergence Analysis}},
  author = {Ba Khiet Le and Minh Thuan Tran and Thi Thanh Tien Pham and Kim Thuong Vo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29552},
  eprint = {2609.29552},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29552},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Reducing the Lipschitz Constant in Tseng Algorithm and the Convergence Analysis
AU  - Ba Khiet Le
AU  - Minh Thuan Tran
AU  - Thi Thanh Tien Pham
AU  - Kim Thuong Vo
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.29552
UR  - https://arxiv.org/abs/2609.29552
AB  - In this paper, we prove the weak and linear convergence of Tseng algorithm applied to the zero of sum of two operators problem where each operator is not necessarily monotone while existing researches in the literature require the monotonicity of both operators. Consequently it allows us to decompose more efficiently and can reduce the Lipschitz constant significantly, which is meaningful especially in big data. Numerical examples supporting the theoretical results are also provided.
ER  -