Non-convex Optimization for Machine Learning

Prateek Jain and Purushottam Kar (2017), "Non-convex Optimization for Machine Learning", Foundations and Trends® in Machine Learning: Vol. 10: No. 3-4, pp 142-363. http://dx.doi.org/10.1561/2200000058
https://www.nowpublishers.com/article/Details/MAL-058
https://www.prateekjain.org/publications/all_papers/JainK17_FTML.pdf
Non-convex Optimization for Machine Learning takes an in-depth look at the basics of non-convex optimization with applications to machine learning. It introduces the rich literature in this area, as well as equipping the reader with the tools and techniques needed to analyze these simple procedures for non-convex problems.
Non-convex Optimization for Machine Learning is as self-contained as possible while not losing focus of the main topic of non-convex optimization techniques. Entire chapters are devoted to present a tutorial-like treatment of basic concepts in convex analysis and optimization, as well as their non-convex counterparts. As such, this monograph can be used for a semester-length course on the basics of non-convex optimization with applications to machine learning. On the other hand, it is also possible to cherry pick individual portions, such the chapter on sparse recovery, or the EM algorithm, for inclusion in a broader course. Several courses such as those in machine learning, optimization, and signal processing may benefit from the inclusion of such topics.
Non-convex Optimization for Machine Learning concludes with a look at four interesting applications in the areas of machine learning and signal processing and explores how the non-convex optimization techniques introduced earlier can be used to solve these problems.