  This thesis explores a particular class of distributed optimization methods
for various separable resource allocation problems, which are of high interest
in a wide array of multi-agent settings. A distinctly motivating application
for this thesis is real-time power dispatch of distributed energy resources for
providing frequency control in a distribution grid or microgrid with high
renewable energy penetration. In this application, it is paramount that agent
data be shared as sparsely as possible in the interest of conserving user
privacy, and it is required that algorithms scale gracefully as the network
size increases to the order of thousands or millions of resources and devices.
Distributed algorithms are naturally well-poised to address these challenges,
in contrast to more traditional centralized algorithms which scale poorly and
require global access to information.
  The class of distributed optimization methods explored here can be broadly
described as Newton-like or second-order, implying utilization of
second-derivative information of the cost functions, in contrast to
well-studied gradient-based or first-order methods. We consider three
formulations of separable resource-allocation problems and develop a
Newton-like algorithm for each. The analysis and simulation studies in the
subsequent chapters demonstrate the advantages of our approaches over existing
methods; most commonly, we note that convergence rates are substantially
improved. We supplement our algorithm development for these three problem
formulations with a network design technique, in which we can construct a
maximally-connected network by adding some edges to the underlying
communication graph, and a real demonstration of distributed algorithms on a
large set of heterogeneous devices on the UC San Diego microgrid.
