How to conditionalize a constraint in mip?

I have an integer variable X that counts down. When it takes the value of zero a binary variable A should take the value 1. Is there a way to do this in Matlab?

Answer 1

[Matt J]

Impose the linear constraints

   A+X>=1

   A<=1-X/Xmax

where Xmax is the maximum value that X can assume.

[Christian Piwitt]

Nice, guess thats exactly what i needed. Will try now. Thanks a lot.

[Nana]

That linear constraints are only applicable for A >= 0, right? What is the constraints if -M <= A <= M ? M is any number. Thanks.

[Matt J]

If A is no longer binary, what are the new rules for its interaction with X?

[Nana]

if a == 0 then b = 1
else b = 0
-M <= a <= M
b={0,1}

[Matt J]

I don't see any X's in there...

[Nana]

I thought a is similar with X, but then I realized X is count-down integer, not continuous variable. Anyway, do you still any idea to solve it? Thanks.

Answer 2

[Matt J]

Decompose into 2 sub-problems.

1. A version of the original problem where A is fixed at 0, and a lower bound of 1 is applied to X
2. A version of the original problem where X is fixed at 0 and A is fixed at 1.

Then see which sub-problem produces the more optimal value.