= Maximum-entropy regularization functional
{title2=$E(x)=\int_\Omega(x\log x-x)$}
This <convex function> penalizes positive densities using negative entropy, with $0\log0=0$ and infinite value for negative inputs. Its scalar derivative is $\log x$ on $x>0$. On a bounded domain, restricting to uniformly positive bounded functions gives a simple setting for a <Fréchet derivative>. Its <Bregman distance> is the <generalized Kullback–Leibler divergence>. With fixed total mass, minimizing this negative-entropy expression maximizes the corresponding entropy.
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