I have an optimization problem that I am unclear whether my answer is write 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.