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 minima at all.

How can I solve this and what is the problem?

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?

There is nothing much to add to the title. 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 minima at all.

How can I solve this and what is the problem?

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 minima at all.

How can I solve this and what is the problem?