PDHCG: A Scalable First-Order Method for Large-Scale Competitive Market Equilibrium Computation
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909641243361280 |
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| author | Liu, Huikang Huang, Yicheng Li, Hongpei Ge, Dongdong Ye, Yinyu |
| author_facet | Liu, Huikang Huang, Yicheng Li, Hongpei Ge, Dongdong Ye, Yinyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PDHCG: A Scalable First-Order Method for Large-Scale Competitive Market Equilibrium Computation Liu, Huikang Huang, Yicheng Li, Hongpei Ge, Dongdong Ye, Yinyu Optimization and Control 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. |
| title | PDHCG: A Scalable First-Order Method for Large-Scale Competitive Market Equilibrium Computation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2506.06258 |