Given an expression:
$$\arg\min_x -\alpha p^TAx + f(x)$$
I'd like to define $v$ such that:
$$\text{prox}_{\sigma f}(v) = \arg\min_x 0.5 \|x - v\|_2^2 + \sigma f(x) = \arg \min_x -\alpha p^TAx + f(x)$$
I abuse equality above to mean the same argument.
How can I find such $v$?
Such trick is done in:
