In this paper, we present a distributed algorithm utilizing the proximal alternating direction method of multipliers (ADMM) in conjunction with sequential constraint tightening to address mixed-integer quadratic programming (MIQP) problems associated with traffic light systems and connected automated vehicles (CAVs) in mixed-traffic intersections. We formulate a comprehensive MIQP model aimed at optimizing the coordination of traffic light systems and CAVs, thereby fully capitalizing on the advantages of CAV integration under conditions of high penetration rates. To effectively approximate the intricate multi-agent MIQP challenges, we develop a distributed algorithm that employs proximal ADMM for solving the convex relaxation of the MIQP while systematically tightening the constraint coefficients to uphold integrality requirements. The performance of our control framework and the efficacy of the distributed algorithm are rigorously validated through a series of simulations conducted across varying penetration rates and traffic volumes.

13 pages