My homework contains a word (freely-translated) "target-function" that I should generate somehow for 9x9 sudoku solver with some MILP problem. But I am bit lost what they mean. I have sofar described the problem as below. Is this the target function for MILP problem (apparently meaning mixed integer linear problem or something like that)?
\begin{cases} \forall r\in {1,2,...,9}\sum_{c=1}^{9}V_{rc}=45 \\ \forall c\in{1,2,...,9}\sum_{r=1}^{9}V_{rc}=45 \\ \forall r\in{1,2,...,9}\forall n\in {1,2,...,9} \sum_{c=1}^{9}x_{rcn} = 1 \\ \forall c\in{1,2,...,9}\forall n\in{1,2,...,9}\sum_{r=1}^{9}x_{rcn} = 1 \ \end{cases}
where $x_{rcn}$ is a binary function with $r$ for row, $c$ for column and $n$ for number between 1 and 9. $V_{rc}$ means the number $n$ in the position $(r,c)$. When I look at wikipedia about the mathematics of sudoku here, I am worried that my way of formulating the problem is not right at all. When I google for MILP, I do not get descriptive hits -- what does this MILP function thing mean?
I have not yet understood how I can formulate the above messy formulates more elegantly, perhaps with the group tabels...sorry I am bit puzzled with the tables in the wikipedia article.