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Nope. I thought about subderivative too... but then I realized this isn't even true. Constructing a counterexample is trivial: y = x if x > 0 else x if x < 0
by mehrdadn 9y ago
Nope. I thought about subderivative too... but then I realized this isn't even true. Constructing a counterexample is trivial:
y = x if x > 0 else x if x < 0 else 0
Zero is in no way a subderivative at x = 0.
- OisinMoran 9y agoYeah 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.
- mehrdadn 9y ago> 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.