I am reading this tutorial that uses ADMM:
https://waller-lab.github.io/DiffuserCam/tutorial/algorithm_guide.pdf
The objective function that needs to be minimized and the augmented Lagrangian is written as
The primal update for the variable v in the document is then given as:
I had expected the primal update to have the fourth, sixth, and the eighth terms of the objective function expression i.e. Eq. 4 as well, as they have the variable v, but clearly I am missing something. Why are these terms not included in the primal update expression?