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?