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Peer-reviewedCC BY 4.0Mathematics

Dynamic Event-Triggered Distributed Online Optimization Subject to Long-Term Constraints

  • Menghui Xiong1,2
  • Zhixian Chen1
  • Qingyi Liu3
  • Yushun Tan3
  1. 1School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China
  2. 2Power Quality Engineering Research Center, Ministry of Education, Anhui University, Hefei 230039, China
  3. 3School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China
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Abstract

This paper investigates distributed online optimization with long-term constraints over time-varying unbalanced multi-agent networks under limited communication resources. To address network imbalance, communication overhead, and the computational burden of per-round constrained projections, a dynamic event-triggered distributed online optimization algorithm with long-term constraints is developed. The algorithm combines an auxiliary-variable-based weighting scheme for column-stochastic networks, a dynamic event-triggered communication protocol, and a long-term constraint mechanism that permits projection onto a simple superset of the original feasible set. We establish bounds on dynamic regret and cumulative absolute constraint violation, both of which explicitly depend on the time horizon and the path variation of the benchmark sequence. Under appropriate parameter choices and sufficiently slow-growing path variation, both bounds are sublinear. Numerical experiments on distributed online linear regression illustrate the theoretical properties of the proposed algorithm.

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Cite

BibTeXRIS
BibTeX
@article{xiong2026dynamic,
  title = {{Dynamic Event-Triggered Distributed Online Optimization Subject to Long-Term Constraints}},
  author = {Menghui Xiong and Zhixian Chen and Qingyi Liu and Yushun Tan},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203728},
  url = {https://www.mdpi.com/2227-7390/14/20/3728},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Dynamic Event-Triggered Distributed Online Optimization Subject to Long-Term Constraints
AU  - Menghui Xiong
AU  - Zhixian Chen
AU  - Qingyi Liu
AU  - Yushun Tan
PY  - 2026
DA  - 2026/10/14
JO  - Mathematics
DO  - 10.3390/math14203728
UR  - https://www.mdpi.com/2227-7390/14/20/3728
AB  - This paper investigates distributed online optimization with long-term constraints over time-varying unbalanced multi-agent networks under limited communication resources. To address network imbalance, communication overhead, and the computational burden of per-round constrained projections, a dynamic event-triggered distributed online optimization algorithm with long-term constraints is developed. The algorithm combines an auxiliary-variable-based weighting scheme for column-stochastic networks, a dynamic event-triggered communication protocol, and a long-term constraint mechanism that permits projection onto a simple superset of the original feasible set. We establish bounds on dynamic regret and cumulative absolute constraint violation, both of which explicitly depend on the time horizon and the path variation of the benchmark sequence. Under appropriate parameter choices and sufficiently slow-growing path variation, both bounds are sublinear. Numerical experiments on distributed online linear regression illustrate the theoretical properties of the proposed algorithm.
SN  - 2227-7390
ER  -