  Distributed optimization, where the computations are performed in a localized
and coordinated manner using multiple agents, is a promising approach for
solving large-scale optimization problems, e.g., those arising in model
predictive control (MPC) of large-scale plants. However, a distributed
optimization algorithm that is computationally efficient, globally convergent,
amenable to nonconvex constraints and general inter-subsystem interactions
remains an open problem. In this paper, we combine three important
modifications to the classical alternating direction method of multipliers
(ADMM) for distributed optimization. Specifically, (i) an extra-layer
architecture is adopted to accommodate nonconvexity and handle inequality
constraints, (ii) equality-constrained nonlinear programming (NLP) problems are
allowed to be solved approximately, and (iii) a modified Anderson acceleration
is employed for reducing the number of iterations. Theoretical convergence
towards stationary solutions and computational complexity of the proposed
algorithm, named ELLADA, is established. Its application to distributed
nonlinear MPC is also described and illustrated through a benchmark process
system.
