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

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.

[Crazy Cool]

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?

Answer 1

[Titus Edelhofer]

Hi,

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).

Titus

[Crazy Cool]

Maximizing for 10^-sum(x(i)*Vect_i) for varying ranges of i, the constraints being A*x>=b BUT I want to put a range on x and let it be within that range OR 0. Is this possible?

[Crazy Cool]

Having a variable in this situation that would either be one number or another, say 0 or 2... would that be possible?

[Steven Lord]

How many variables do you have and how many of them need to have this 0 OR in-a-range behavior? If the number of variables that you need to constrain this way is small, solve the problem with the first set to 0 and the rest allowed to vary normally, then the second set to 0 and the rest varying normally, then the first two set to 0 and the rest varying normally, etc. Once you've solved those subproblems, take the one with the best result.

[Crazy Cool]

Yeah I need this to work to a scalable amount of variables. Is there a way I can manipulate the nonlin constraint side to make this work? Each variable comes in with a range AND they can all also be set to 0. A few have just 1 value they can be other than 0.

[Crazy Cool]

Do you have any ideas on how I might be able to do this?