# Logical operators in constrained optimization

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?
• I'm confused about this question. Is the answer to your question: "Yes, it is the minimum of the values $\{ f(1,4,2), f(4,1,3), f(9,7,6)\}$"? Also are $b$ and $c$ the same as $y$ and $z$? If your question was not answered by the first statement, perhaps consider expanding and clarifying your question. – jgon Mar 28 at 23:06
• sorry I edited the question. $y$ and $z$ were meant – Jamal B. Mar 28 at 23:15
• $y=4=1$ What system are you working in which allows this? – Bertrand Wittgenstein's Ghost Mar 28 at 23:19