In this post you will see how to linearize max functions, min functions, and absolute value functions. These can be expressed mathematically as:
Let’s start with the modulus, as the other two depend on it.
Here you simply replace that one constraint by the following two:
The min function can be linearized as:
First, we decompose the min function into a max and a modulus.
Then we get rid of the max.
Finally, the answer is using the following five constraints:
Remember to penalize and such that only one of them will be different from zero in any solution.
The max function can be linearized as follows:
From here on things are very similar to the min function…
And finally, the five necessary constraints are:
And again, remember to penalize and .
Thanks to Lieke van der Heide.
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