When using fmincon can I have a variable be constrainted by either a range OR zero?

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Essentially could I have a variable be between 5 and 20 OR be 0. The way I currently have it when I apply the range 5 to 20 I lose the ability for the solution to work at 0. Is there another optimization I can use for this? Thanks.
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Crazy Cool
Crazy Cool on 25 Jul 2017
An additional comment: I have a series of variables and need to be over 1 and under 20 but the can not be chosen to use and thus also could be 0, how could I do this?

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Answers (1)

Titus Edelhofer
Titus Edelhofer on 25 Jul 2017
programmatically: yes, you can always formulate something like this as a non linear constraint. But the optimizer (and the theory behind) doesn't like the variable to jump. Let's say you have a value of 5. The optimizer (somewhat simplified:) ) looks in the neighborhood of the current point for a better solution, but will never do the jump to the zero.
Is your problem non linear so that you have to use fmincon? If it was linear, then intlinprog would be suitable to handle such cases through adding additional variables (and using integer variables).

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