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@jemoka / Jemoka Knowledge Base / wiki/concepts/conjugate_function.md
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--- 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 \(\text{sup}_{x} = \max_{x}\))