Symmetric Bregman distance
= Symmetric Bregman distance
{title2=$D_J^{\mathrm{sym}}(u,v)=\langle p_u-p_v,u-v\rangle$}
For $p_u\in\partial J(u)$ and $p_v\in\partial J(v)$, add the two <Bregman distances> to get $D_J^{p_v}(u,v)+D_J^{p_u}(v,u)=\langle p_u-p_v,u-v\rangle\geq0$. The choice of <subgradients> matters. This is generally not a metric: it need not separate points or satisfy a <triangle inequality>.