@Gillee 

Thanks for your answer.
This is interesting... Maybe calling LLSolve function multiple times, adding the previous result as the initialpoint for the next call can be a good way to get better results.

However, I finally managed to get better results by resizing my equations (the D values were really close to 0 so I just added a 1000 factor)

Thanks a lot @phil2 for your detailed answer. However I can't find any attached worksheet, where should I get the attached files ?

Admittedly, this still doesn't quite explain why the new minimum is actually larger.  However, considering that, as you pointed out, the constraints were redundant to begin with, the notion of feasibility tolerance makes those constraints inadvisable anyway.

The problem is that sometimes (depending on the system, which is not always the exact same one as list_1 or list_2) LSSolve comes out with negatives values as D, and I would like to make sure that it never happens, and I guess there is now other way to do that than adding positive constraints. Maybe playing with the feasability tolerance option could lead me to better results?

@phil2 

I am really sorry, I attached the wrong list of equations..

Here is the worksheet :
 

Download worksheet_help(1).mw

I don't understand, why when adding constraints for List_1, i get a worse result.
List_2 should be resolvable as well, but the result I get without any constraint is not correct (D36 is negative), and when I add positive constraints, LSSolve returns an error....

I am using Maple 2016.0