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