The unit commitment problem (UCP) is the problem of deciding up/down and generation-level patterns of energy production units. Due to the expansion of distributed energy resources and the liberalization of energy trading in recent years, solving the distributed UCP (DUCP) is attracting the attention of researchers. Once an up/down pattern is determined, the generation-level pattern can be decided distributively using the alternating direction method of multipliers (ADMM). However, ADMM does not guarantee convergence when deciding both up/down and generation-level patterns. In this paper, we propose a method to solve the DUCP using ADMM and constraint optimization programming. Numerical experiments show the efficacy of the proposed method.