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--- title: "Robust Optimization" source: https://www.jemoka.com/posts/kbhrobust_optimization/ --- 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}\qty(a_{i}^{T} x \leq b_{i}) \geq \eta, i = 1 \dots m \end{align}