I have an optimization problem that I am unclear whether my answer is right or not:

$$ 
(1) min_{x} \frac{1}{2}\left \| Ax-b \right \|_2^2
\\
s.t. \  \  \Phi v=x  \ , \ {x^T(1-x)}=0
$$

A and $\Phi$ are matrices and x, b and v are vectors. Is there a way to use ADMM and variable splitting to solve this optimization problem? The final answer for $x$ should have binary {0,1} values only, since the operator $A$ only accepts binary inputs.