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PreprintCC BY 4.0arXiv

Parameter-Free First-Order Method for Constrained Variational Inequalities

  • Yan Wu
  • Qi Luo
  • Yuyuan Ouyang
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Abstract

Constrained variational inequalities (VIs) provide a general framework for modeling and solving complementarity and equilibrium problems with functional constraints. In this paper, we propose a parameter-free accelerated operator sliding (PFAOS) method for solving monotone VIs with convex smooth constraints. For a single constraint, PFAOS achieves an operator evaluation complexity of π’ͺ(1/Ξ΅) and a constraint gradient evaluation complexity of π’ͺ(1/√Ρ), without requiring prior knowledge of the Lipschitz constant of the VI operator or the smoothness constant of the constraint function. We further extend PFAOS to multiple constraints by incorporating a primal-dual hybrid gradient update, yielding a multi-constrained PFAOS (MC-PFAOS) method that preserves the same evaluation complexities. Finally, numerical experiments are conducted on large-scale games with coupling constraints to validate the efficiency and effectiveness of the proposed algorithms.

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Cite

BibTeXRIS
BibTeX
@misc{wu2026parameterfree,
  title = {{Parameter-Free First-Order Method for Constrained Variational Inequalities}},
  author = {Yan Wu and Qi Luo and Yuyuan Ouyang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00229},
  eprint = {2611.00229},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00229},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Parameter-Free First-Order Method for Constrained Variational Inequalities
AU  - Yan Wu
AU  - Qi Luo
AU  - Yuyuan Ouyang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00229
UR  - https://arxiv.org/abs/2611.00229
AB  - Constrained variational inequalities (VIs) provide a general framework for modeling and solving complementarity and equilibrium problems with functional constraints. In this paper, we propose a parameter-free accelerated operator sliding (PFAOS) method for solving monotone VIs with convex smooth constraints. For a single constraint, PFAOS achieves an operator evaluation complexity of π’ͺ(1/Ξ΅) and a constraint gradient evaluation complexity of π’ͺ(1/√Ρ), without requiring prior knowledge of the Lipschitz constant of the VI operator or the smoothness constant of the constraint function. We further extend PFAOS to multiple constraints by incorporating a primal-dual hybrid gradient update, yielding a multi-constrained PFAOS (MC-PFAOS) method that preserves the same evaluation complexities. Finally, numerical experiments are conducted on large-scale games with coupling constraints to validate the efficiency and effectiveness of the proposed algorithms.
ER  -