Decomposition of Nonconvex Optimization via Bi-Level Distributed ALADIN

Decentralized optimization algorithms are of interest in different contexts, e.g., optimal power flow or distributed model predictive control, as they avoid central coordination and enable decomposition of large-scale problems. In case of constrained nonconvex problems, only a few algorithms are currently available-often with limited performance or lacking convergence guarantee. This article proposes a framework for decentralized nonconvex 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 quadratic program (QP) by decentralized algorithms. We provide sufficient conditions for local convergence while allowing for inexact decentralized/distributed solutions of the coordination QP. Moreover, we show how decentralized variants of conjugate gradient and alternating direction of multipliers method (ADMM) can be employed at the inner level. We draw upon examples from power systems and robotics to illustrate the performance of the proposed framework.