Recent Advances in Robust Optimization

Abstract

This paper provides an overview of developments in robust optimization since 2007. It seeks to give a representative picture of the research topics most explored in recent years, highlight common themes in the investigations of independent research teams and highlight the contributions of rising as well as established researchers both to the theory of robust optimization and its practice. With respect to the theory of robust optimization, this paper reviews recent results on the cases without and with recourse, i.e., the static and dynamic settings, as well as the connection with stochastic optimization and risk the- ory, the concept of distributionally robust optimization, and findings in robust nonlinear optimization. With respect to the practice of robust optimization, we consider a broad spectrum of applications, in par- ticular inventory and logistics, finance, revenue management, but also queueing networks, machine learning, energy systems and the public good. Key developments in the period from 2007 to present include: (i) an extensive body of work on robust decision-making under uncertainty with uncertain dis- tributions, i.e., ‘‘robustifying’’ stochastic optimization, (ii) a greater connection with decision sciences by linking uncertainty sets to risk theory, (iii) further results on nonlinear optimization and sequential deci- sion-making and (iv) besides more work on established families of examples such as robust inventory and revenue management, the addition to the robust optimization literature of new application areas, especially energy systems and the public good