Sudoku and absolute value equation

I know there is many mathematical way to reformulate the Sudoku problem. I'm wondering if there is a way to reformulate this problem as an absolute value equation :

$$Ax + B|x|=b$$ where x and b $\in \mathbb{R}^n$, A and B $\in \mathbb{R}^{n \times n}$

• What do you want to achieve with the absolute value? I would expect solution space to be positive integers 1-9 anyway. I'd also expect integer coefficients in A and B. – Pieter21 Jan 14 '15 at 11:35
• I'm looking for application of this kind of equation. Also x depend on reformulation, so I guess it's not necesseraly positive integer 1-9. – Tanj Jan 14 '15 at 12:49