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.

中文翻译：

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通过双层分布式ALADIN分解非凸优化

分散式优化算法在不同的情况下是有意义的，例如，最佳潮流或分布式模型预测控制，因为它们避免了中央协调并能够分解大规模问题。在出现约束非凸问题的情况下，当前只有几种算法可用-通常性能有限或缺乏收敛保证。本文提出了一种通过增强拉格朗日交替方向不精确牛顿（ALADIN）算法的双层分布进行分散式非凸优化的框架。双层分布意味着将外部ALADIN结构与内部分布/分散级别组合在一起，通过分散算法解决ALADIN凸协调二次程序（QP）的压缩变体。我们为本地收敛提供了充分的条件，同时允许协调QP的不精确分散/分布式解决方案。此外，我们展示了如何在内部使用共轭梯度和乘方交替方向的分散变体方法（ADMM）。我们从电力系统和机器人技术中获取示例，以说明所提出框架的性能。