In recent years, the large increase in connected devices and the data that are collected by these devices have caused a heightened interest in distributed processing. Many practical distributed networks are of heterogeneous nature, because different devices in the network can have different specifications. Because of this, it is highly desirable that algorithms operating within these networks can operate asynchronously, since in that case there is no need for clock synchronisation between the nodes, and the algorithm is not slowed down by the slowest device in the network. In this paper, we focus on the primal-dual method of multipliers (PDMM), which is a promising distributed optimisation algorithm that is suitable for distributed optimisation in heterogeneous networks. Most theoretical work that can be found in existing literature focuses on synchronous versions of PDMM. In this work, we prove the convergence of stochastic PDMM, which is a general framework that can model variations such as asynchronous PDMM and PDMM with transmission losses.@en

In this work, we analyse a stochastic version of the primaldual method of multipliers (PDMM), which is a promising algorithm in the field of distributed optimisation. So far, its convergence has been proven for synchronous implementations of the algorithm [1], [2]. Simulations have shown that PDMM also converges if it is implemented asynchronously, having the advantage that there is no need for clock synchronisation between the nodes in a distributed network. Furthermore, a broadcast implementation of asynchronous PDMM can be derived, instead of the usual unicast implementation. This broadcast implementation comes with a number of benefits...@en