TITLE: Optimize absolute value $\min |x| + |y|$
QUESTION [0 upvotes]: How do you convert $\min |x| + |y|$ to a linear program?
Is this method correct?
$$\min w + z$$
$$w >= x$$
$$w >= -x$$
$$z >= y$$
$$z >= -y$$

REPLY [2 votes]: Yes, this is a correct linearization. An alternative approach introduces two nonnegative values and one equality constraint for each absolute value.  See this post for both approaches.
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