Optimization problem with integer variables

I have a nXn matrix M of integers with values 1...k. All the occurrences of values in M can be counted using hist(). My constraint is as follows : non of the occurrences of each value in M should not exceed a certain bound c. How do I define such constraint using intlinprog ?

Answer 1

[Torsten]

Let x(i,j,l) (1<=i,j<=n, 1<=l<=k) a binary variable which is 1 if the element at position (i,j) equals l, 0 else.

Then the constraints are

sum_i sum_j x(i,j,l) <= c for 1<=l<=k
0 <= x(i,j,l) <= 1 
x(i,j,l) integer.

Best wishes

Torsten.

[Aviram Zilberman]

Thank you for your quick answer. One more question:how does this fit into linprog() ?

[Torsten]

It's not clear to me what you are aiming at in the end.

Do you want to generate all possible (nxn) matrices M with integer values from 1 to k as coefficients which satisfy the constraint you mention ?

Best wishes

Torsten.

[Aviram Zilberman]

I need to do the following : 1. position k transmitters in a binary vector x of length n s.t x(i)=1 if a transmitter is located in position i and 0 otherwise. Given 2. Given a binary matrix A(nXn) of receivers s.t A(i,j)=1 if a receiver is located in position(i,j) and 0 otherwise. 3. each receiver is matched with an exclusive transmitter, s.t each transmitter is matched with up to c receivers. The optimization function is : find a match between receivers and transmitters, and a placement for the k transmitters s.t the total distance between transmitters and receivers is minimal.

Thanks for your generous help !