Logical operators in constrained optimization

Question

Trying to find the minimum of a function $f(x,y,z)$ is it possible to write (and solve) such constraints:
$min f(x,y,z)$
subject to $(x=1 \land y=4 \land z=2) \lor (x=4 \land y=1 \land z=3) \lor (x=9 \land y=7 \land z=6)$
If it is possible, which method can be used for it? Is it even feasible for e.g. 100k of such or statements? Surely I could calculate $f(x,y,z)$ for all the 100k combinations and pick the minimum, but this doesn't scale very well, is there a more performant way, even if it's an approximation?
Thanks in advance.