2025/06/06 by Huikang Liu, Liu, Huikang, Yicheng Huang +7 · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2506.06258
openalex publication_date 2025/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.