---
title: "conjugate function"
type: concept
source: https://www.jemoka.com/posts/kbhconjugate_function/
confidence: high
status: active
---

The conjugate of a function \(f\) is \(f^{*}\qty(y) = \text{sup}_{x \in \text{dom }f} \qty(y^{T}x - f\qty(x))\). \(f^{*}\) is convex, even if \(f\) is not.
(fyi \(\text{sup}_{x} = \max_{x}\))
