The efficacy of robust optimization methods has recently been extended to multistage problems with uncertainties bound in predetermined sets. Although current frameworks are general and model a large variety of settings, they cannot accurately describe problems with changing uncertainties. This is instrumental in many applications, because our knowledge about the uncertainties changes throughout the process.
In this talk, we take a step toward generalizing robust optimization approaches to problems with varying uncertainty sets. Extending the pioneering work of Ben-Tal, Goryashko, Guslitzer, and Nemirovski (2004), we provide tractable reformulations for both types of uncertainties, namely for exogenous and endogenous sets. We discuss the optimization of radiation therapy plans in the presence of changing hypoxia in clinical cancer cases. This framework encompasses a broad range of real-world applications, in which the first-stage decisions are typically from a countable set, e.g., in machine learning, facility location, knapsack, and routing problems, to name a few.
Omid Nohadani is an Associate Professor in the department of Industrial Engineering and Management Sciences at Northwestern University. His primary area of research is robust optimization in convex and nonconvex problems. Nohadani’s applied work addresses a variety of settings: cancer therapy, statistics, machine learning, nano-technology, ultrafast optics, high-performance computing, and vehicle routing. More recently, his interests have focused on the area of healthcare engineering, both from the methodological as well as treatment design aspect. He received his Diploma degree in mathematical physics from the University of Bonn, Germany and a Ph.D. in theoretical physics
from the University of Southern California. He was a postdoctoral researcher at the Operations Research Center at MIT and a research fellow and instructor at Harvard Medical School.
Discovery Building, Orchard View Room