Jerry Chua

Despite significant progress in optimization under uncertainty, deterministic optimization remains the dominant approach in practice. Although solutions from deterministic models are often brittle in the face of uncertainty, models that account for uncertainty are frequently too complex to implement and maintain. The budgeted uncertainty set, introduced by Bertsimas and Sim (2004), offers a streamlined and practically effective framework for some linear optimization problems and has been widely cited in the literature. However, extending this approach to broader decision settings, especially those involving adaptive recourse decisions or non-linear convex structures, remains a challenge. In this paper, we propose a streamlined framework for enhancing robustness in decision models by ensuring that constraints are satisfied as reliably as possible under uncertain outcomes. Our formulation, grounded in the L_1-norm to quantify deviations of input parameters from their nominal values, yields tractable robust counterparts without relying on dualization or approximation techniques. This results in a unified and implementable framework for addressing dynamic and nonlinear decision problems. We illustrate the practical effectiveness of our approach through a numerical study on the AC optimal power flow problem, showing that it achieves superior robustness and computational efficiency compared to both deterministic and stochastic benchmarks.

Inverse optimization (IO) has emerged as a powerful framework for analyzing prescriptive model parameters that rationalize observed or prescribed decisions. Despite the prevalence of discrete decision-making models, existing work has primarily focused on continuous and convex models, for which the corresponding IO problems are far easier to solve. This paper makes three contributions that broaden the foundations and applications of inverse optimization in discrete decision-making. First, we propose a new approach for approximating the inverse-feasible region of solutions to discrete optimization problems by modifying their linear relaxations. Second, we integrate these modified relaxations with existing methods to develop a unified framework for solving IO problems. Finally, through the lens of inverse optimization, we provide a fresh perspective on the sensitivity analysis of prescriptive solutions to discrete optimization problems, and demonstrate the computational advantages of our models and algorithms.