On the Effect of Norm Selection in Scenario Approach to Robust Feasibility Problem

Abstract

In this paper, we investigate the effect of norm selection in the scenario approach to robust feasibility problems. Robust feasibility problems can be converted into robust optimization problems by minimizing an objective function such as the norm of decision variables. In such cases, the choice of the norm may affect the robustness of the optimal solution in the scenario approach. The 2- and ∞-norms are compared by simulating two numerical examples, which represent two extremal situations for minimizing ∞-norm.