2
$\begingroup$

I would like to know which are the advantage to do not convert quadratic expressions into linear expression in MiniZinc. For example let be the following simple MiniZinc code

var -1.0..1.0:  x1;
var -1.0..1.0:  y1;
constraint (x1*y1) = 1.0;
solve satisfy;

The flatzinc code of that portion of code is

var -1.0..1.0: x1:: output_var;
var -1.0..1.0: y1:: output_var;
var -1.0..1.0: X_INTRODUCED_0_ ::var_is_introduced :: is_defined_var;
constraint float_eq(X_INTRODUCED_0_,1.0);
constraint float_times(x1,y1,X_INTRODUCED_0_):: defines_var(X_INTRODUCED_0_);
solve  satisfy;

As you can see, the quadratic term x1*y1 is still quadratic float_times(x1,y1,X_INTRODUCED_0_). Why MiniZinc does not convert x1*y1 to linear constraints?

$\endgroup$

1 Answer 1

4
$\begingroup$

What formulation do you expect MiniZinc to produce?

MiniZinc does not convert x1 * y1 = 1 to a linear constraint because x1 * y1 = 1 cannot be represented by a linear constraint.

$\endgroup$
1
  • $\begingroup$ +1 If you allow an addition binary variable, I believe you can linearize the constraint given the variables are required to be between -1 and 1: $x_1+y_1=4z-2$ where $z$ is binary. If the product of $x_1$ and $y_1$ should be one, they should both be 1 or $-1$. Hence, their sum should be either $2$ or $-2$. $\endgroup$
    – Sune
    Oct 15, 2022 at 16:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.