---
title: "Geometric Interperattion of the Dual"
source: https://www.jemoka.com/posts/kbhgeometric_interperattion_of_the_dual/
---

Let \(\mathcal{G} = \qty {f_{1}\qty(x), f_{0}\qty(x) \mid x \in \mathcal{D}}\) be the set of achievable constraint/objective pairs. The Lagrange Dual Function \(g\qty(\lambda) = \text{inf}_{t,u \in G} \qty(t + \lambda u)\).
We will push this line all the way down, and then push up its slope as much as possible.
