Norm induced polyhedral uncertainty sets for robust linear optimization

In this paper, we study uncertainty set construction for robust optimization using various polyhedral norms. We first introduce the classical symmetric polyhedral-norms induced uncertainty sets and the corresponding robust counterparts of a linear uncertain constraint. Then, we introduce a novel method for asymmetric uncertainty set construction based on the distributional information of the uncertain parameters. Deterministic robust counterpart formulations for both types of uncertainty sets are derived for a general linear uncertain constraint. We further derive the robust counterpart of a linear uncertain constraint where the uncertain parameters belong to (i) an intersection of two symmetric uncertainty sets and (ii) an intersection of asymmetric and symmetric uncertainty sets. Using a numerical example and a reactor design problem, we demonstrate that appropriate uncertainty set construction reduces solution conservativeness. We also highlight the significance of integrating the data and distributional information of uncertain parameters in terms of safeguarding feasibility alongside improving the solution.