  This paper reviews recent advances in the field of optimization under
uncertainty via a modern data lens, highlights key research challenges and
promise of data-driven optimization that organically integrates machine
learning and mathematical programming for decision-making under uncertainty,
and identifies potential research opportunities. A brief review of classical
mathematical programming techniques for hedging against uncertainty is first
presented, along with their wide spectrum of applications in Process Systems
Engineering. A comprehensive review and classification of the relevant
publications on data-driven distributionally robust optimization, data-driven
chance constrained program, data-driven robust optimization, and data-driven
scenario-based optimization is then presented. This paper also identifies
fertile avenues for future research that focuses on a closed-loop data-driven
optimization framework, which allows the feedback from mathematical programming
to machine learning, as well as scenario-based optimization leveraging the
power of deep learning techniques. Perspectives on online learning-based
data-driven multistage optimization with a learning-while-optimizing scheme is
presented.
