cplex - minimization and sum of matrix values and indexes

Question

I'm using a Cplex Java API for the first time.

I want to minimize the sum of values in matrix on some indexes, which is given by condition.

For example, if I have the matrix M = {{ 0, 1, 2, 1},{ 1, 2, 1, 0},{ 0, 1, 1, 0},{ 1, 1, 1, 2}} .

I want to calculate two sums, first, the sum of all elements e = 1 and second, indexes where elements are equal to 1 .

So, indexes where element is equal 1 are {{0,1} {1,0} {1,2} {2,1} {2,2} {3,0} {3,1} {3,2} .

Result for first case is 9 (1+1+1+1+1+1+1+1+1)` and for second case is 24 (0+1+1+0+1+2+2+1+2+2+3+0+3+1+3+2).

I'm not sure how to use IloNumVar[] and create an expression using IloLinearNumExpr which is used in sum and minimize a function, while matrix M is type int[][] .

Answer 1

In your problem description, there is nothing to optimize. All elements in your matrix M are constant. So the two sums you described can be computed directly without involving a tool like CPLEX.