Suppose you have two functions $f_1$ and $f_2$ and you know the minimum and the maximum values of each function. What's a good upperbound for the minimum value of $f_1+f_2$? I thought $\min(\min(f_1)+\max(f_2),\max(f_1)+\min(f_2))$, what do you think?
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it seems the best possible, with so little information – Denis Jul 02 '13 at 11:19
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Now, suppose that instead of having the exact maximum and minimum values of the functions, you have the upperbounds, would it still work? – Filippo Bistaffa Jul 02 '13 at 11:42