Böcker i Foundations and Trends (R) in Optimization-serien

Reviews the information relaxation approach which works by reducing a complex stochastic Dynamic Programming to a series of scenario-specific deterministic optimization problems solved within a Monte Carlo simulation.

This book is an introduction to Acceleration Methods used in convex optimization that enables the reader to quickly understand the important principles and apply the techniques to their own research.

Explores a class of methods that are capable of formally verifying properties of deep neural networks. The book introduces a unified mathematical framework for verifying neural networks, classify existing methods under this framework, provide pedagogical implementations of existing methods, and compare those methods on a set of benchmark problems.

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.

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.

Examines dynamic trading of a portfolio of assets in discrete periods over a finite time horizon, with arbitrary time-varying distribution of asset returns. The goal is to maximize the total expected revenue from the portfolio, while respecting constraints on the portfolio like a required terminal portfolio and leverage and risk limits.