Optimization under Uncertainty with Applications in Data-driven Stochastic Simulation and Rare-event Estimation

by Xinyu Zhang

For many real-world problems, optimization could only be formulated with partial information or subject to uncertainty due to reasons such as data measurement error, model misspecification, or that the formulation depends on the non-stationary future. It thus often requires one to make decisions without knowing the problem's full picture. This dissertation considers the robust optimization framework—a worst-case perspective—to characterize uncertainty as feasible regions and optimize over the worst possible scenarios. Two applications in this worst-case perspective are discussed: stochastic...