Convex Optimization for Big Data

TL;DR

This paper reviews recent convex optimization techniques tailored for Big Data, emphasizing scalable algorithms, approximation methods, and parallel computation to overcome computational and storage challenges.

Contribution

It provides a comprehensive overview of emerging convex optimization algorithms for Big Data, highlighting simple principles and significant accelerations.

Findings

Scalable first-order and randomized methods improve efficiency.

Parallel and distributed algorithms enhance computational speed.

New algorithms achieve significant acceleration on classical problems.

Abstract

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.