Tell me if I have found the right approach to the following optimization problem:

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

$A$ and $\Phi$ represent matrices, $x$, $b$ and $v$ vectors. The final answer for $x$ should have binary {0,1} values only, since the operator $A$ only accepts binary inputs. 

Will ADMM and variable splitting solve this?