1
$\begingroup$

I need to find the value and positions of the global minima of a 6 parameter rational function. My current try is something like

NMinimize[{function[x1, x2, x3, x4, x5, x6], region}, {x1, x2, x3, x4, x5, x6}]

Which gives me one result with which there are two problems:

(1) The presented point is possibly not the only global minimum. How can I get all of them if there is more than one? (I have seen equivalent questions here, but the most important question is the following:)

(2) If I set and change a starting interval for one or more parameters in the search, i.e.

NMinimize[{function[x1, x2, x3, x4, x5, x6], region}, {{x1, x1i, x1f}, x2, x3, x4, x5, x6}]

the value of the minimum changes, which obviously means that earlier presented greater values were not global minima at all.

How can I solve this and what is the problem?

Improve this question
$\endgroup$
6
  • 2
    $\begingroup$ From the documentation: If your function and the constraints are linear, NMinimize will find global minima. Otherwise, NMinimize may sometimes find only a local minimum. Unforutnately you do not share the function or the constraints, so my guess would be that your function is not linear and you were returned a local minimum the first time. Finding a guaranteed global minimum of an arbitrary function is hard. $\endgroup$
    – MarcoB
    Commented Aug 30, 2020 at 2:09
  • 1
    $\begingroup$ Does Minimize[] solve your problem? $\endgroup$
    – Michael E2
    Commented Aug 30, 2020 at 2:55
  • $\begingroup$ Try to use Method->"DifferentialEvolution" $\endgroup$
    – Cesareo
    Commented Aug 30, 2020 at 8:20
  • $\begingroup$ @MarcoB My function is a ratio of multiple variables polynomials. I see! Thank you! $\endgroup$
    – GaloisFan
    Commented Aug 30, 2020 at 17:03
  • $\begingroup$ @MichaelE2 Unfortunately it does not seem like my problem would have an analytical solution. $\endgroup$
    – GaloisFan
    Commented Aug 30, 2020 at 17:03

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.