Bregman iteration
= Bregman iteration
{c}
{title2=$u^{k+1}\in\arg\min_u\{\tfrac12\|Ku-f\|^2+\alpha D_J^{p^k}(u,u^k)\}$}
Starting with $u^0=0$ and $p^0=0\in\partial J(0)$, update $p^{k+1}=p^k+K^*(f-Ku^{k+1})/\alpha$. The optimality condition makes $p^{k+1}\in\partial J(u^{k+1})$. The iteration replaces a fixed penalty by its <Bregman distance> from the preceding iterate and accumulates residual information in the dual variable. The first update uses $k=0$.