---
title: "Duality for Feasible Problems"
type: concept
source: https://www.jemoka.com/posts/kbhduality_for_feasible_problems/
confidence: high
status: active
---

Consider feasible problems.
\begin{align} \min_{x}\quad &amp; 0 \\ \textrm{s.t.} \quad &amp; \dots \end{align}
so the optimal is either \(p^{*} = 0\) or \(p^{*} = +\infty\). And thus the Lagrange Dual Problem boils down to checking if \(d^{*} \geq 0\), if so, then the original problem is&rsquo;nt feasible (since dual gives a lower bound.)
