Distributed Convex Optimization: Based on Monotone Operator Theory

Following their conception in the mid twentieth century, the world of computers has evolved from a landscape of isolated entities into a sprawling web of interconnected machines. Yet, given this evolution, many of the methods we use for allowing computers to work together still reflect their inherently isolated origins with the aggregation of...

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...

Inexact distributed optimization schemes: A convergence analysis using monotone operator theory

Distributed optimization has been an <br/>extensively studied field for years. Recent developments in the area of sensors makes it possible to create networks consisting of a large number of nodes. The focus of this thesis will be optimizing distributed problems over a decentralized network. These distributed optimization schemes operate in an...

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...