Distributed Optimisation with Linear Equality and Inequality Constraints using PDMM

In this article, we consider the problem of distributed optimisation of a separable convex cost function over a graph, where every edge and node in the graph could carry both linear equality and/or inequality constraints. We show how to modify the primal-dual method of multipliers (PDMM), originally designed for linear equality constraints,...

Convergence of Stochastic PDMM

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...

Distributed Optimisation Using Stochastic PDMM: Convergence, transmission losses and privacy

In recent years, the large increase in connected devices and the data that is collected by these devices has caused a heightened interest in distributed processing. Many practical distributed networks are of heterogeneous nature. Because of this, algorithms operating within these networks need to be simple, robust against network dynamics and...

Communication efficient privacy-preserving distributed optimization using adaptive differential quantization

Privacy issues and communication cost are both major concerns in distributed optimization in networks. There is often a trade-off between them because the encryption methods used for privacy-preservation often require expensive communication overhead. To address these issues, we, in this paper, propose a quantization-based approach to achieve...

Two for the price of one: communication efficient and privacy-preserving distributed average consensus using quantization

Both communication overhead and privacy are main concerns in designing distributed computing algorithms. It is very challenging to address them simultaneously as encryption methods required for privacy-preservation often incur high communication costs. In this paper, we argue that there is a fundamental link between communication efficiency...

Derivation and Analysis of the Primal-Dual Method of Multipliers Based on Monotone Operator Theory

In this paper, we present a novel derivation of an existing algorithm for distributed optimization termed the primal-dual method of multipliers (PDMM). In contrast to its initial derivation, monotone operator theory is used to connect PDMM with other first-order methods such as Douglas-Rachford splitting and the alternating direction method...

Quantized Distributed Optimization Schemes: A monotone operator approach

Recently, the effects of quantization on the Primal-Dual Method of Multipliers were studied.<br/>In this thesis, we have used this method as an example to further investigate the effects of quantization on distributed optimization schemes in a much broader sense. Using monotone operator theory, the effect of quantization on all distributed...

Quantization effects in PDMM: A first study for synchronous distributed averaging

Nowadays, large-scale networks of computing units, often characterized by the absence of central control, have become more commonplace in many applications. To facilitate data processing in these large-scale networks distributed signal processing is required. The iterative behaviour of distributed processing algorithms combined with the limited...

On Simplifying the Primal-Dual Method of Multipliers

Recently, the primal-dual method of multipliers (PDMM) has been proposed to solve a convex optimization problem defined over a general graph. In this paper, we consider simplifying PDMM for a subclass of the convex optimization problems. This subclass includes the consensus problem as a special form. By using algebra, we show that the update...

Distributed Convex Optimization: A Study on the Primal-Dual Method of Multipliers

The Primal-Dual Method of Multipliers (PDMM) is a new algorithm that solves convex optimization problems in a distributed manner. This study focuses on the convergence behavior of the PDMM. For a deeper understanding, the PDMM algorithm was applied to distributed averaging and distributed dictionary learning problems. The results were compared...