# An Asynchronous Approximate Distributed Alternating Direction Method of Multipliers in Digraphs

Wei Jiang, Andreas Grammenos, Evangelia Kalyvianaki, Themistoklis Charalambous

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussaConference article in proceedingsScientificvertaisarvioitu

4 Sitaatiot (Scopus)
53 Lataukset (Pure)

## Abstrakti

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.

Alkuperäiskieli Englanti 60th IEEE Conference on Decision and Control, CDC 2021 IEEE 3406-3413 8 978-1-6654-3659-5 https://doi.org/10.1109/CDC45484.2021.9683229 Julkaistu - 2021 A4 Artikkeli konferenssijulkaisussa IEEE Conference on Decision and Control - Austin, YhdysvallatKesto: 13 jouluk. 2021 → 17 jouluk. 2021Konferenssinumero: 60

### Julkaisusarja

Nimi Proceedings of the IEEE Conference on Decision and Control 2021-December 0743-1546 2576-2370

### Conference

Conference IEEE Conference on Decision and Control CDC Yhdysvallat Austin 13/12/2021 → 17/12/2021

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