  As problems in machine learning, smartgrid dispatch, and IoT coordination
problems have grown, distributed and fully-decentralized optimization models
have gained attention for providing computational scalability to optimization
tools. However, in applications where consumer devices are trusted to serve as
distributed computing nodes, compromised devices can expose the optimization
algorithm to cybersecurity threats which have not been examined in previous
literature. This paper examines potential attack vectors for generalized
distributed optimization problems, with a focus on the Alternating Direction
Method of Multipliers (ADMM), a popular tool for convex optimization. Methods
for detecting and mitigating attacks in ADMM problems are described, and
simulations demonstrate the efficacy of the proposed models. The weaknesses of
fully-decentralized optimization schemes, in which nodes communicate directly
with neighbors, is demonstrated, and a number of potential architectures for
providing security to these networks is discussed.
