Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints

This paper considers a multiblock nonsmooth nonconvex optimization problem with nonlinear coupling constraints. By developing the idea of using the information zone and adaptive regime proposed in [J. Bolte, S. Sabach and M. Teboulle, Nonconvex Lagrangian-based optimization: Monitoring schemes and global convergence, Mathematics of Operations Research, 43: 1210--1232, 2018], we propose a multiblock alternating direction method of multipliers for solving this problem. We specify the update of the primal variables by employing a majorization minimization procedure in each block update. An independent convergence analysis is conducted to prove subsequential as well as global convergence of the generated sequence to a critical point of the augmented Lagrangian. We also establish iteration complexity and provide preliminary numerical results for the proposed algorithm.