Proximal ADMM for nonconvex and nonsmooth optimization

By enabling the nodes or agents to solve small-sized subproblems achieve coordination, distributed algorithms are favored by many networked systems for efficient and scalable computation. While convex problems, substantial available, results more broad nonconvex counterparts extremely lacking. This paper develops a algorithm class of nonsmooth problems featured (i) objective formed both separate composite components regarding decision variables interconnected agents, (ii) local bounded constraints, (iii) coupled linear constraints. problem is directly originated from smart buildings also in other domains. To provide with convergence guarantee, we revise powerful alternating direction method multiplier (ADMM) proposed proximal ADMM. Specifically, noting that main difficulty establish optimization ADMM assume boundness dual updates, propose update discounted manner. leads establishment so-called sufficiently decreasing lower Lyapunov function, which critical convergence. We prove converges some approximate stationary points. besides showcase efficacy performance numerical example concrete application multi-zone heating, ventilation, air-conditioning (HVAC) control buildings.