Network optimization problems arise naturally as a way of encoding the coordination task entrusted to multi-agent systems deployed in many areas of engineering, including power, communication, transportation, and swarm robotics. The large-scale nature of these systems coupled with the intrinsic modularity in their structure due to the technological advances in communication, embedded computing, and parallel processing requires a shift from the traditional paradigm of centralized decision-making to a distributed one. This transition, which is essential to harness the true capabilities of modern cyberphysical systems, raises a number of noteworthy challenges as well as opportunities, and has sparked the development of solutions that scale with the number of agents, provide plug-and-play capabilities, and are resilient against single points of failure. Motivated by these considerations, this thesis is a contribution to the growing body of work that deals with the synthesis and analysis of provably correct algorithmic solutions to structured network problems.

Specifically, the thesis is divided into two parts. The first part focuses on synthesizing algorithmic solutions for application-agnostic large-scale network problems. We consider constrained optimization problems where the global objective function is the aggregate of local objectives of the participating agents; the collective goal of the agents and the underlying interaction pattern among them define the constraints. Using continuously differentiable exact penalty functions and globally projected dynamical systems, we then propose privacy-preserving, scalable, accelerated and anytime algorithms to solve these optimization problems. The second part is application-oriented and deals with constrained optimization problems in the context of power systems. In particular, we focus on the utilization of distributed energy resources for frequency regulation in the modern grid. We design distributed time-invariant controllers stabilizing the time-varying power dynamics for primary frequency control, and develop meaningful abstractions for groups of distributed energy resources to participate in the secondary frequency control market.