The zero finding problem that the Douglas-Rachford Splitting (DRS) Algorithm attempts to solve has the following formulation
$0 \in (A+B)(x)$
where $A$ and $B$ are maximal monotone operators. Then, the DRS algorithm finds the corresponding zero of the equation above by splitting the computations using resolvents $J_{\alpha A}$ and $J_{\alpha B}$ as:
$ x^{k + \frac{1}{2}} = J_{\alpha B}(z^K)$
$ x^{k + 1} = J_{\alpha A}(2*x^{k + \frac{1}{2}} - z^k)$
$ z^{k + 1} = z^{k} + x^{k + 1} - x^{k + \frac{1}{2}}$,
which is clear. Now, my problem is how do we extend this algorithm if the zero finding problem has a constant offset so the problem can be written as
$cte \in (A+B)(x)$
where $cte$ is a constant value.