Cost function with regularization.
\[\begin{split}J(x) = \\frac{1}{2}(x - x_0)^T S_0^{-1}(x - x_0) + λ\\frac{1}{2}(z - Hx - c)^T S_z^{-1}(z - Hx - c)\end{split}\]
Note: S_z has already been scaled by the regularization factor gamma during initialization.