Re: [Help-glpk] Modeling SOS1

[Andrew Makhorin]

> I would like to model an SOS1 constraints in GLPK . 
> In my case, {U, B} and {V, X} are SOS1 sets. U,B are non-negative
> variables and X is a boolean variable.
>  

SOS1(x1, x2, ..., xn) means that at most one of the variables can be
non-zero.

If all the variables are binary, SOS1 is equivalent to

   x[1] + x[2] + ... + x[n] <= 1

If the variables are continuous, assuming that 0 <= x[j] <= u[j], where
u[j] is an upper bound of x[j], SOS1 can be modeled as follows:

   x[j] <= u[j] * z[j]  for j = 1,...,n,

   z[1] + ... + z[n] <= 1,

where z[j] are auxiliary binary variables.