Originally posted by: SystemAdmin

Hi,
I have a code of form:

IloCplex model = null;
IloNumVar X[] = null;
IloNumVar E[] = null;
IloNumVar E_abs = model.numVarArray(noOfRev, 0, 10);
 X = model.numVarArray(noOfVar, -5, 5);
 E = model.numVarArray(noOfRev, -10, 10);

After this I have numerous constraint for both X and E

my optimization (minimization) expression should be of the form

model.addMinimize(model.scalProd(E_abs, cost));

where
E_abs[i]=|E[i]| for all i,

i.e the absolute value.

For this i cannot apply the abs() method since it will make the equation linear num expression, which will make it impossible to add it to optimization equation.
So, I need some constraints which ensures that E_abs[i]=Abs(E[i]).

And also the value of E[i] should determine E_abs[i] not the other way around. i.e I need the value of E[i] first and then only get its absolute value to put in the optimization equation..

Been stuck with this for quite a while, looked into some other post for absolute value but somehow could not implement it write......
Any help will be highly appreciated.

I am using the Java concert for CPLEX 12 academic edition

Regards
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

If cost[i] >= 0 for all i, then there is an easy trick to do what you want: just state the objective function in terms of E_abs, the constraints in terms of E, and then add the following inequalities for all i:

E_abs[i] >= E[i]
E_abs[i] >= -E[i]

These inequalities ensure that E_abs[i] >= |E[i]|. Now, because cost[i] >= 0, there is no reason for E_abs[i] to get larger than |E[i]|. Hence, in every optimal solution you will have E_abs[i] == |E[i]|.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Thanks a lot for the help...
#CPLEXOptimizers
#DecisionOptimization