@misc{liu_pdhcg_2025,
 abstract = {Large-scale competitive market equilibrium problems arise in a wide range of important applications, including economic decision-making and intelligent manufacturing. Traditional solution methods, such as interior-point algorithms and certain projection-based approaches, often fail to scale effectively to large problem instances. In this paper, we propose an efficient computational framework that integrates the primal-dual hybrid conjugate gradient (PDHCG) algorithm with GPU-based parallel computing to solve large-scale Fisher market equilibrium problems. By exploiting the underlying mathematical structure of the problem, we establish a theoretical guarantee of linear convergence for the proposed algorithm. Furthermore, the proposed framework can be extended to solve large-scale Arrow-Debreu market equilibrium problems through a fixed-point iteration scheme. Extensive numerical experiments conducted on GPU platforms demonstrate substantial improvements in computational efficiency, significantly expanding the practical solvable scale and applicability of market equilibrium models.},
 author = {Liu, Huikang and Huang, Yicheng and Li, Hongpei and Ge, Dongdong and Ye, Yinyu},
 doi = {10.48550/arXiv.2506.06258},
 file = {Full Text PDF:C\:\\Users\\14532\\Zotero\\storage\\VSKV7SUF\Łiu 等 - 2025 - PDHCG A Scalable First-Order Method for Large-Scale Competitive Market Equilibrium Computation.pdf:application/pdf;Snapshot:C\:\\Users\\14532\\Zotero\\storage\\J3GYG7JF\\2506.html:text/html},
 keywords = {Mathematics - Optimization and Control},
 month = {June},
 note = {arXiv:2506.06258 [math]},
 publisher = {arXiv},
 shorttitle = {PDHCG},
 title = {PDHCG: A Scalable First-Order Method for Large-Scale Competitive Market Equilibrium Computation},
 url = {http://arxiv.org/abs/2506.06258},
 urldate = {2025-06-17},
 year = {2025}
}