Linearizing a nonlinear constraint for use in intlinprog

Hello Everyone,

I'm setting up an integer linear program using the "Problem-based approach". I have several constraints of the form:

Where:

x: is a binary decision variable, defined using "optimvar".

y: is a continious variable, defined using "optimexpr"

C: a constant real number.

I have tried to resolve this by creating an extra optimization expression "z" and then describing the product in several linear constraints as shown below.

 constr1 = z <= M* x;           % M is a big M constant
 constr2 = z <= y;              % y is an optimexpr described elsewhere in the code
 constr3 = z >= y - M*(1- x);   
 constr4 = z >=0;
 constr5 = z <= C;

However, when I apply it, and use the function "show" to chek on the constraints, this is what I get:

" Constraint with all zero coefficients"

Could someone point me to what I'm missing here?

[Matt J]

However, when I apply it, and use the function "show" to chek on the constraints, this is what I get:

Well, you wouldn't have been able to examine a constraint using show(). You would need showconstr() for that...

I also don't understand why you would be using optimexpr to create y. Isn't y an independent variable? If so, you should use optimvar to create y as well.

[Hatim Mala]

Hey Matt,

Thanks for your help!

1. I am actually using: write(Prob.Constraints.constr2) which creates a .txt file containing the constraint formula. Still I get "Constraint with all zero coefficients".

2. y is not an independent variable, y itself depends on a linear combination of other decision variables. Hence the use of "optimexpr".

[Matt J]

Well, I suggest attaching a .mat file containing x,y,z,C so that we can try to reproduce what you're seeing.