Nonconvex Optimization for Big Data Analysis: Theory and Practice

A. M.-C. So

Optimization is now widely reckoned as an indispensable tool in big data analysis. Although convex optimization remains a powerful, and is by far the most extensively used, paradigm for tackling big data applications, we have witnessed a shift in interest to non-convex optimization techniques over the last few years. Given the potential of non-convex optimization techniques for dealing with big data applications, our goal is to elucidate common structures that are present in the non-convex formulations of various applications from machine learning, signal processing, and statistics, and to demonstrate how such structures can be exploited in the design and analysis of numerical methods that are suitable for large-scale problems.