I want to minimize the following function. It has two variable, $x$ and $y$ are real. I want proof the global optimality. But the feasible region of the variables are disjoint. My question is, how can I proof the GLOBAL optimality of the solution?
$ \min f(x,y) = x^2+ y^2. $ s.t., $ 10\leq x\leq 20 $ $ 30\leq x\leq 40 $ $ 15\leq y\leq 25 $ $ 70\leq y\leq 86 $
Please help on this.