Two approaches to handling uncertainty. Consider an LP:
\begin{align} &\min c^{T}x \\ &s.t. a_{i}^{x} \leq b_{i} \end{align}
what if our constraints are uncertain. Both of these reduce to an SOCP. See slides. Deterministic Worst-Case \begin{align} &\min c^{T}x \ &s.t.\ a_{i}^{T} x \leq b_{i}, \forall a_{i} \in \epsilon_{i} \end{align} Stochastic \begin{align} &\min c^{T}x \ &s.t.\ \text{prob}\left(a_{i}^{T} x \leq b_{i}\right) \geq \eta, i = 1 \dots m \end{align}