$$\sum_{j=3q-2}^{3q}\sum_{i=3p-2}^{3p}x_{ijk}=1, \forall k = 1 :n; p,q = 1:3$$
The above constraint wants to describe what condition in the Sudoku problem?
I think the constraint here is that the numbers $1$ to $9$ appear exactly once on each square $3 \times 3$, but I think there is a small mistake in the constraint.
That's right: this expresses the box constraint (assuming, given the other constants, that n=9).
i.e., we have k in 1:9 indexing digits, p in 1:3 indexing bands, and q in 1:3 indexing stacks. The sums have (i,j) ranging over the (row,col) coordinates of the cells in the intersection of band p and stack q. The constraint expresses that digit k occurs exactly once in that box.
