Originally posted by: Liebe

Hi everyone,

I want to use sos2 to solve my problem. But I have a question about sos2.

The definition is:

 SOS Type 2 is a set of variables where at most two variables may be nonzero. If two variables are nonzero, they must be adjacent in the set.

For example:

I have 4 variables: x1, x2, x3 and x4. There are 2 nonzero variables.

The solution may be: x1 und x2 or x2 und x3 or x3 und x4.

Because of adjacent, the solution cannot be x1 und x3 or x2 und x4.

Is that right?

Thanks!

Yes, that is right. Notice however that SOS2 does not require two variables to be non-zero. It only says that at most two can be non-zero and if two are non-zero then they must be adjacent. So the singletons x1 or x2 or x3 or x4 would also be feasible in your case, as would be a solution in which all four vairables are 0.

Originally posted by: Liebe

Thanks for your answer.

Dose that mean: the constraint x1+x2+x3+x4<=2 cannot be written as a sos2 because of "adjacent".

Because in my constraint x1 und x3 can be nonzero simultaneously.

Correct. "x1+x2+x3+x4<=2" allows solutions x1!=0 and x3!=0, while "{x1,x2,x3,x4} is SOS2" does not allow this type of solution. So the two constraints are different.