A Bregman inertial iteratively regularized extragradient method for bilevel variational inequality problems
Abstract
In this paper, we consider bilevel variational inequality problems, where the feasible set is the solution set of another variational inequality. We propose a Bregman inertial regularized extragradient method for solving these problems. By performing the inertial extrapolation in the dual space, the proposed method aligns the inertial step with the structure of the Bregman three-point identity. We also derive explicit non-asymptotic bounds for the generalized gap function. More precisely, using diminishing regularization, we establish convergence rates of 𝒪(1/k1−b) for the optimality gap and 𝒪(1/kb) for the feasibility gap with $ 0 < b< 1$. For constant regularization parameter η>0, we establish an 𝒪(1/k) rate for the optimality gap and an 𝒪(1/k)+𝒪(η) bound for the feasibility gap. Furthermore, numerical experiments on traffic networks and multi-portfolio Nash equilibrium problems demonstrate the practical effectiveness of the proposed framework.
Related
- Regularized extragradient method for structured bilevel optimization in continuous and discrete time
- Extragradient and Past Extragradient Methods for (L0,L1)-Lipschitz Variational Inequalities
- Parameter-Free Adaptive Extragradient Methods for Generalized-Smooth Variational Inequalities
- Variational Contraction Conditions for Iterative Algorithms in Multi-Population Discrete-Time Regularized Mean-Field Games
- Rényi-Regularized Flow-Based Variational Inference for Bayesian Calibration
BibTeX
@misc{chen2026bregman,
title = {{A Bregman inertial iteratively regularized extragradient method for bilevel variational inequality problems}},
author = {Kangming Chen and Atsushi Hori and Ellen H. Fukuda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30898},
eprint = {2609.30898},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30898},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A Bregman inertial iteratively regularized extragradient method for bilevel variational inequality problems
AU - Kangming Chen
AU - Atsushi Hori
AU - Ellen H. Fukuda
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.30898
UR - https://arxiv.org/abs/2609.30898
AB - In this paper, we consider bilevel variational inequality problems, where the feasible set is the solution set of another variational inequality. We propose a Bregman inertial regularized extragradient method for solving these problems. By performing the inertial extrapolation in the dual space, the proposed method aligns the inertial step with the structure of the Bregman three-point identity. We also derive explicit non-asymptotic bounds for the generalized gap function. More precisely, using diminishing regularization, we establish convergence rates of 𝒪(1/k^1−b) for the optimality gap and 𝒪(1/k^b) for the feasibility gap with $ 0 < b< 1$. For constant regularization parameter η>0, we establish an 𝒪(1/k) rate for the optimality gap and an 𝒪(1/k)+𝒪(η) bound for the feasibility gap. Furthermore, numerical experiments on traffic networks and multi-portfolio Nash equilibrium problems demonstrate the practical effectiveness of the proposed framework.
ER -