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Yeah you're right, the subdifferential of f(x)=|x| at the origin is the interval [−1, 1].

In the fourth paragraph of link [1] in the above post they explain quite well why we can get away with this type of trickery even if it seems wrong.



> Yeah you're right, the subdifferential of f(x)=|x| at the origin is the interval [−1, 1].

I'm confused where you're seeing absolute value? I never had absolute value anywhere. The second example I wrote just amounted to y = x.




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