So I have the following matrix:
\begin{equation} P_{i,j}= \begin{bmatrix} x_0 & x_1 & x_2 \\ y_0 & y_1 & y_2 \\ z_0 & z_1 & z_2 \end{bmatrix} \end{equation}
where each of the elements in the matrix are binary variables (can be either 0 or 1). I am solving an optimization problem where I want to impose a constraint where each of the rows of the matrix have to have $n$ number of zeros. So for example, for the first row of matrix $P$ (containing the $x_i$ elements), I want to enfore that for this row, I want one of these $x_i$'s to be zero (but not explicitly stating which one should be zero). As a second example, for the second row of matrix $P$ (containing the $y_i$ elements), I want to enfore that for this row, I want two of these $y_i$'s to be zero (but not explicitly stating which ones should be zero). And so fourth...
Is there a way to make this kind of formulation? I was thinking of imposing the constraints as follows:
$\sum_j P_{1,j} = 2$
$\sum_j P_{2,j} = 1$
Would this be the correct approach?
Your help would be much appreciated!
