A Decentralised Asynchronous Optimisation Algorithm with an Application to Phase Retrieval - Mafakheri, Behnam; Manton, Jonathan H.; Shames, Iman (Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop, 2024)
This paper tackles the challenge of decentralised, nonconvex optimisation in situations where agents work asynchronously. Our main contribution is a new algorithm, partially asynchronous ADMM, designed to solve decentralised optimisation problems like phase retrieval. Importantly, it does not require a central coordinator and can work with arbitrary connected network setups. We also prove that our algorithm is equivalent to the randomised block coordinate Douglas-Rachford Splitting method. To illustrate the algorithm's effectiveness, we provide numerical results for the distributed phase retrieval problem, demonstrating its correctness and performance.