## Abstract

In this work, we consider the asynchronous distributed optimization problem in which each node has its own convex cost function and can communicate directly only with its neighbors, as determined by a directed communication topology (directed graph or digraph). First, we reformulate the optimization problem so that Alternating Direction Method of Multipliers (ADMM) can be utilized. Then, we propose an algorithm, herein called Asynchronous Approximate Distributed Alternating Direction Method of Multipliers (AsyAD-ADMM), using finite-time asynchronous approximate ratio consensus, to solve the multi-node convex optimization problem, in which every node performs iterative computations and exchanges information with its neighbors asynchronously. More specifically, at every iteration of AsyAD-ADMM, each node solves a local convex optimization problem for the one of the primal variables and utilizes a finite-time asynchronous approximate consensus protocol to obtain the value of the other variable which is close to the optimal value, since the cost function for the second primal variable is not decomposable. If the individual cost functions are convex, but not-necessarily differentiable, the proposed algorithm converges at a rate of O(1/k), where k is the iteration counter. The efficacy of AsyAD-ADMM is exemplified via a proof-of-concept distributed least square optimization problem with different performance-influencing factors investigated.

Original language | English |
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Title of host publication | 60th IEEE Conference on Decision and Control, CDC 2021 |

Publisher | IEEE |

Pages | 3406-3413 |

Number of pages | 8 |

ISBN (Electronic) | 9781665436595 |

DOIs | |

Publication status | Published - 2021 |

MoE publication type | A4 Article in a conference publication |

Event | IEEE Conference on Decision and Control - Austin, United States Duration: 13 Dec 2021 → 17 Dec 2021 Conference number: 60 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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Volume | 2021-December |

ISSN (Print) | 0743-1546 |

### Conference

Conference | IEEE Conference on Decision and Control |
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Abbreviated title | CDC |

Country/Territory | United States |

City | Austin |

Period | 13/12/2021 → 17/12/2021 |

## Keywords

- asynchronous ADMM
- directed graphs
- Distributed optimization
- finite-time consensus
- ratio consensus