 Bregman iteration

Starting with $u^0=0$ and $p^0=0\in \partial J(0)$, update $p^{k+1}=p^k+K^{\ast }(f-K{u}^{k+1})/\alpha$. 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 $k=0$.