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.