Consider the Robust Approximation problem:

Robust Approximation

Minimize \(\norm{Ax - b}\) with uncertain \(A\); two approaches—

1. stochastic: minimize \(\mathbb{E}\norm{Ax -b }\)
2. worst-case: set \(\mathcal{A}\) of possible values of \(A\), minimize \(\text{sup}_{A \in A} \norm{Ax - b}\)