Add a constraint to Ax>b using intlinprog

I have a matrix A with m rows (eq's) and n columns (variable) where Ax>b; each row in A has a specific value in b. I want to add a constraint related to the sum of the elements in a certain column to be greater than a value (to be added to the end of b). In other words, a certain variable (ex: x1) should exist in the equations no more than certain times given by the corresponding b. Is it possible to do so? I have read some papers have solved the same problem but without details. Any idea? Thanks in advance

[Torsten]

But the matrix A is given, I guess, and the elements of A determine whether x1 is present in an equation or not. So how should it be possible to deduce a constraint for what you are asking for ?

Best wishes

Torsten.

[Ismaeel]

Thanks Torsen... Yes, that's right, A is given. But, in MILP problems, one can add auxiliary variables that choose the rows (or even columns) that optimize the problem. Say, you want to ask Matlab that either equation 1 is correct or equation2 but not both. Matlab will choose the best one that minimizes the total cost. However, I can not apply this idea in Matlab.

Answer 1

[Alan Weiss]

You might be able to use the formulation of semicontinuous constraints in this example. Or the Set the Generator Startup Variables idea.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Ismaeel]

Thanks Alan