Infimal convolution
= Infimal convolution
{title2=$E\mathbin\square F$}
The <infimal convolution> is $(E\mathbin\square F)(u)=\inf_v\{E(v)+F(u-v)\}$. It optimizes a decomposition of $u$ between two costs. It is <convex> when both costs are <convex functions>, and its <convex conjugate> is $E^*+F^*$ whenever the extended-real operations are well defined.