Originally posted by: SystemAdmin

[ArushGadkar said:]

Hello All,
I have a variable vector A and B (both binary) a certain length.
I want to define a new vector C[j] = min(A[j],B[j])

I want to implement this condition in Cplex. Is the following logic
correct:

For each j implement the constraints

C[j] <=  A[j]  and C[j] <= B[j]<br />
Similarly now if i have to define C = max ( X , 0 )
would the following be correct:

C>=  0 and C >= X.
I think the above equations would hold true only depending if we are maximizing/minimizing. Is there a general form to express min/max constraints independent of what we do with the objective function.
Your help is kindly appreciated.

Thanks
Arush.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

[notdarkyet said:]

Of course you are modeling C<= min(A,B) and C >= max(A,B) respectively. So you enlarge the feasible set and your C will be correct only if
i)  there is a C being feasible with C = min(A,B) and
ii) you are maximizing some expressions where all C[i] have positive coeffs (or negative for tha max-case)

If you do not maximize the C's and you want to have the min(A,B) you'll need disjunctive inequalities and an additional binary variable for every i (see e.g. Nemhauser/Wolsey).

#CPLEXOptimizers
#DecisionOptimization