# Decomposition of non-convex optimization via bi-level distributed ALADIN

## TL;DR

This paper introduces a bi-level distributed framework for non-convex optimization that combines ALADIN with decentralized algorithms, providing convergence guarantees and practical case studies in power systems and robotics.

## Contribution

It presents a novel bi-level distribution approach for decentralized non-convex optimization using ALADIN, with convergence analysis and implementation via decentralized algorithms.

## Key findings

- Proves local convergence under certain conditions.
- Demonstrates effectiveness in power systems and robotics case studies.
- Shows how decentralized algorithms can solve the inner coordination problem.

## Abstract

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.