A Bregman proximal linearized ADMM for fractional programming with nonlinear coupling constraints

@misc{liu2026bregman,
  title = {{A Bregman proximal linearized ADMM for fractional programming with nonlinear coupling constraints}},
  author = {Pengjie Liu and Jinhu Chen and Minh N. Dao and Hu Shao and Jinbao Jian},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11961},
  eprint = {2610.11961},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11961},
}

TY  - UNPB
TI  - A Bregman proximal linearized ADMM for fractional programming with nonlinear coupling constraints
AU  - Pengjie Liu
AU  - Jinhu Chen
AU  - Minh N. Dao
AU  - Hu Shao
AU  - Jinbao Jian
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11961
UR  - https://arxiv.org/abs/2610.11961
AB  - This paper considers a nonconvex fractional optimization problem with composite structure and nonlinear equality constraints. We reformulate the problem as a non-fractional min-max problem with corresponding optimal solutions. By linearizing the nonlinear constraint terms in the augmented Lagrangian and incorporating Bregman proximal linearization and a relaxation factor in $(0, 2)$ into the alternating direction method of multipliers (ADMM), we develop a Bregman proximal linearized ADMM with guaranteed subsequential convergence to a lifted critical point. Convergence of the entire sequence is established under the Kurdyka--Łojasiewicz (KL) property. We further derive convergence rates under either a Hölderian value proximity error bound condition or the KL property, with the corresponding exponent in $[0, 1)$. In particular, we establish superlinear convergence for exponents in $(0, 1/2)$, together with finite, linear, and sublinear convergence in the remaining cases. Numerical experiments demonstrate the effectiveness of the proposed algorithm.
ER  -