A Unified Theory of Robust and Distributionally Robust Optimization via the Primal-Worst-Equals-Dual-Best Principle

Abstract

A Primal-Worst-Equals-Dual-Best Perspective on Robust and Distributionally Robust Optimization In the paper “A Unified Theory of Robust and Distributionally Robust Optimization via the Primal-Worst-Equals-Dual-Best Principle,” Jianzhe Zhen, Daniel Kuhn, and Wolfram Wiesemann develop a generalized “primal-worst-equals-dual-best” principle that establishes strong duality between semi-infinite primal worst and nonconvex dual best formulations of robust and distributionally robust nonlinear optimization problems. Their theory offers an alternative characterization of (distributionally) robust optimization problems that bypasses the need to mobilize the machinery of abstract semi-infinite duality theory. The paper will be of interest to researchers and practitioners in the field of optimization under uncertainty.