How to linearize if, then constraint.

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Solution 1

$$\begin{array}{l} y-z\leq (1-x)M\\ z-y\leq (1-x)M \end{array} $$

where $M$ is a sufficiently large constant.

Solution 2

One way to do it is to enforce $$x(y-z) = 0$$ since this implies that $x=0$ or $y-z=0$. Note, however, that this is not a linear constraint...

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mahdi
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Updated on May 23, 2020

Comments

  • mahdi
    mahdi over 3 years

    I want to model the following constraint:

    • $x$ is a binary variable,
    • $y$ and $z$ are positive variables,
    • if $x=1$ then $y=z$.

    I want to code this constraint in Gams.