Continuous optimization is a key component of modern data analysis. Recently, the demands
of extremely large-scale applications have shifted the focus from high cost, high accuracy
methods to low cost, moderate accuracy methods that scale to billions of variables. These
large-scale problems often have a decomposable structure that can be exploited by low cost
methods in order to yield parallel and distributed algorithms. This talk discusses some of the
best performing low-cost methods for large-scale optimization problems with structure, outlines
several challenges, and discusses future research directions in this rapidly developing area.