---
title: "Robust Optimization"
type: concept
source: https://www.jemoka.com/posts/kbhrobust_optimization/
confidence: high
status: active
---

Two approaches to handling uncertainty. Consider an LP:
\begin{align} &amp;\min c^{T}x \\ &amp;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} &amp;\min c^{T}x \\ &amp;s.t.\ a_{i}^{T} x \leq b_{i}, \forall a_{i} \in \epsilon_{i} \end{align}
Stochastic \begin{align} &amp;\min c^{T}x \\ &amp;s.t.\ \text{prob}\qty(a_{i}^{T} x \leq b_{i}) \geq \eta, i = 1 \dots m \end{align}
