Re: [Help-glpk] Compare two matrices

[Andrew Makhorin]

> I have the following problem: I have a parameter A with (3 indices)
> and a decision variable X also with 3 indices (same matrix form).
> The idea is as follows: Parameter A is the old matrix, X is the new
> matrix. Now I need to be sure that at most 10 changes are made. So I
> would like to have at most 10 different X[a,b,c] to A[a,b,c] for all
> a,b,c.

> Now I was used to programs that could work with absolute values
> (SUM[a,b,c]: abs(A[a,b,c]-X[a,b,c]) <= 10), however GLPK is not able
> to work with absolute values of decision variables.

> Does anyone have an idea how to solve this?

> I tried introducing a Dummy: D[a,b,c] = 1 for A[a,b,c]<=X[a,b,c], 0
> else but that didn't work out....

Big M formulation:

"if z1 then x <= a - eps else x <= +M" can be modeled as

   x <= (a - eps) * z1 + M * (1 - z1)

"if z2 then x >= a + eps else x >= -M" can be modeled as

   x >= (a + eps) * z2 - M * (1 - z2)

"if z then x <= a - eps or x >= a + eps else a - eps < x < a + eps"
is equivalent to "z = z1 or z2" and can be modeled as

   0 <= 2 * z - z1 - z2 <= 1

where z1, z2, z are binary variables.