Historically, scalability has been a major challenge for the successful application of
semidefinite programming in fields such as machine learning, control, and robotics. In this …

The power flow equations relate the power injections and voltages in an electric power
system and are therefore key to many power system optimization and control problems …

Chordal and factor-width decomposition methods for semidefinite programming and
polynomial optimization have recently enabled the analysis and control of large-scale linear …

In recent years, optimization theory has been greatly impacted by the advent of sum of
squares (SOS) optimization. The reliance of this technique on large-scale semidefinite …

The sparse portfolio selection problem is one of the most famous and frequently studied
problems in the optimization and financial economics literatures. In a universe of risky …

We devise a scheme for solving an iterative sequence of linear programs (LPs) or second
order cone programs (SOCPs) to approximate the optimal value of any semidefinite program …

It is well-known that any sum of squares (SOS) program can be cast as a semidefinite
program (SDP) of a particular structure and that therein lies the computational bottleneck for …

The alternating current optimal power flow (ACOPF) problem optimizes the generation and
the distribution of electric energy taking into account the active and the reactive power …

We present a framework for bounding extreme values of quantities on global attractors of
differential dynamical systems. A global attractor is the minimal set that attracts all bounded …

Many large-scale systems have inherent structures that can be exploited to facilitate their
analysis and design. This thesis investigates how chordal graph properties can be used to …