  Decentralized optimization algorithms are important in different contexts,
such as distributed optimal power flow or distributed model predictive control,
as they avoid central coordination and enable decomposition of large-scale
problems. In case of constrained non-convex optimization only a few algorithms
are currently are available; often their performance is limited, or they lack
convergence guarantees. This paper proposes a framework for decentralized
non-convex optimization via bi-level distribution of the Augmented Lagrangian
Alternating Direction Inexact Newton (ALADIN) algorithm. Bi-level distribution
means that the outer ALADIN structure is combined with an inner
distribution/decentralization level solving a condensed variant of ALADIN's
convex coordination QP by decentralized algorithms. We prove sufficient
conditions ensuring local convergence while allowing for inexact
decentralized/distributed solutions of the coordination QP. Moreover, we show
how a decentralized variant of conjugate gradient or decentralized ADMM schemes
can be employed at the inner level. We draw upon case studies from power
systems and robotics to illustrate the performance of the proposed framework.
