Convex optimization has emerged useful tool for applications that include data analysis and model fitting resource allocation, engineering design, network design, and optimization, finance, and control signal processing.

After an overview of the mathematics, algorithms, and software framworks for covex optimization, we turn to common themes that arise across applications, such as sparsity and relaxation.

We describe recent work on real-time embedded convex optimization, in which small problems are solved repeatedly in milisecond or micosecond time frams, and large-sclae distributed convex optimization, in which many solvers are coordinated to solve enormous problems.