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I have a function of six variables, a known function, say y= F(x1, x2, x3, x4, x5, x6). I know the ranges of these variables: a1<x1<b1, a2<x2<b2, a3<x3<b3, a4<x4<b4, a5<x5<b5, a6<x6<b6. Is it possible to figure out whether a certain value of this function is reached for any set of the variables. I suspect that a certain value of y, say y0=10^{-12} can be achieved for at least one set of variables x1, x2, x3, x4, x5, x6. is it possible to find this set in Mathematica?

neutrino
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1 Answers1

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I would try:

Assuming[{a1<x1<b1, ...},
FindInstance[f(x1,...,x6) == desiredValue, {x1,...,x6}]]

If you give us your full problem (with details), we can better help you.

David G. Stork
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  • thank you David. This works but takes too much time. Is there a way that I can use to speed up the process? Can a new command be added to the already existing ones to achieve this goal? – neutrino Dec 01 '22 at 17:54
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    @neutrino: Why oh why do you need a new command?? The several hours it would take you to write and debug the code is MUCH longer than simply typing the above. – David G. Stork Dec 16 '22 at 00:27