For example, when I am trying to minimize the function $f(x) = x^2 - 6x +12$ where $x\geq$ are non negative real number. If by some way, I was able to obtaining the upper bound (only) or lower bound (only) of this problem but without knowing the corresponding $x$, for example like knowing that min $f(x)$ is less than $3.5$.
Would there be any methods that could help exploit this information to reach the optimal point quickly than usual.
In this case, the optimal solution for this problem would be that $Min \ f(x) = 3$ at $x=3$
Thank you very much