PDHCG: A Scalable First-Order Method for Large-Scale Competitive Market Equilibrium Computation

TL;DR

This paper introduces a scalable primal-dual hybrid conjugate gradient method combined with GPU computing to efficiently solve large-scale market equilibrium problems, with proven linear convergence and broad applicability.

Contribution

It presents a novel, efficient computational framework that significantly improves scalability and convergence guarantees for large-scale market equilibrium computations.

Findings

Achieves substantial speedups on GPU platforms.

Successfully solves larger market problems than previous methods.

Provides theoretical linear convergence guarantees.

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.