Books in the Foundations and Trends (R) in Optimization series

An atomic decomposition provides a description of the most informative features of a solution or a kind of generalized principal component analysis. In this book, the authors describe the rich convex geometry that underlies atomic decomposition and demonstrate its use in practical examples.

Presents a comprehensive statistical learning framework that uses Distributionally Robust Optimization (DRO) under the Wasserstein metric to ensure robustness to perturbationsin the data. The authors introduce the reader to the fundamental properties of the Wasserstein metric and the DRO formulation, before explaining the theory in detail.