  This article reviews recent advances in convex optimization algorithms for
Big Data, which aim to reduce the computational, storage, and communications
bottlenecks. We provide an overview of this emerging field, describe
contemporary approximation techniques like first-order methods and
randomization for scalability, and survey the important role of parallel and
distributed computation. The new Big Data algorithms are based on surprisingly
simple principles and attain staggering accelerations even on classical
problems.
