On the continuity assumption of 'Finite Adaptability in Multistage Linear Optimization' by Bertsimas and Caramanis

Two-stage robust optimization is a fundamental paradigm for modeling and solving optimization problems with uncertain parameters. A now classical method within this paradigm is finite-adaptability, introduced by Bertsimas and Caramanis (IEEE Transactions on Automatic Control, 2010). In this note, we point out that the continuity assumption they stated to ensure the convergence of the method is not correct, and we propose an alternative assumption for which we prove the desired convergence.