# how can I proof the GLOBAL optimality of a problem where the feasible region is disjoint?

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., $$10\leq x\leq 20$$ $$30\leq x\leq 40$$ $$15\leq y\leq 25$$ $$70\leq y\leq 86$$

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Do you mean "region" instead of "resign?" Not sure what "feasible resign" means. –  Thomas Andrews Dec 10 '12 at 18:53
@ThomasAndrews: you are right, I meant region. I edited text. Thanks for informing me. –  fayzur Dec 10 '12 at 19:05
I answered speculatively but it would help if you told us what you already know about solving the problem when the feasible region is not like this. (P.S. your use of "disjoint" is incorrect here; a set cannot be disjoint on its own, it has to be disjoint from another set. I guessed in my answer that you meant "not connected", i.e. consisting of several separated components.) –  Ben Millwood Dec 10 '12 at 19:16