I have to solve the following problem, and I don't know how to proceed: $$\min \{(x-a)^2 + (y-b)^2+xy\}$$ subject to $0 \leq x \leq 1, \ 0 \leq y \leq 1$.
I have tried to use Lagrangian multipliers but, I am not sure how to put the conditions $0 \leq x \leq 1, \ 0 \leq y \leq 1$ on them.