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...