Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints
This addresses optimization challenges in fields like machine learning and engineering, but it is incremental as it extends existing ADMM methods to more complex settings.
The paper tackles the problem of multiblock nonsmooth nonconvex optimization with nonlinear coupling constraints by proposing a multiblock ADMM algorithm, proving convergence to a critical point and providing iteration complexity and numerical results.
This paper proposes a multiblock alternating direction method of multipliers for solving a class of multiblock nonsmooth nonconvex optimization problem with nonlinear coupling constraints. We employ a majorization minimization procedure in the update of each block of the primal variables. Subsequential and global convergence of the generated sequence to a critical point of the augmented Lagrangian are proved. We also establish iteration complexity and provide preliminary numerical results for the proposed algorithm.