>> 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. Since z1 and z2 cannot be 1 at the same time, i.e. z1 + z2 <= 1, the latter constraint can be simplified as z = z1 + z2 that allows eliminating z. _______________________________________________ Help-glpk mailing list [email protected] http://lists.gnu.org/mailman/listinfo/help-glpk
