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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.

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    $\begingroup$ 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. $\endgroup$ – jgon Mar 28 at 23:06
  • $\begingroup$ sorry I edited the question. $y$ and $z$ were meant $\endgroup$ – Jamal B. Mar 28 at 23:15
  • $\begingroup$ Look up SAT. SAT is NP-Complete. An optimization problem can be converted into a sequence of SAT problems. Also, look at integer programming. $\endgroup$ – copper.hat Mar 28 at 23:16
  • $\begingroup$ $y=4=1$ What system are you working in which allows this? $\endgroup$ – Bertrand Wittgenstein's Ghost Mar 28 at 23:19
  • $\begingroup$ I've edited it again. @copper.hat will look into it $\endgroup$ – Jamal B. Mar 28 at 23:27

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