Question for exercise 10

Hi,

I have a question about exercise 10.
We are given an expression for the subgradient of a max function as the hint.
And in the solution, after applying the hint, the subgradients is a set of argmax of the dual function. I do not get it. Could you please elaborate a little bit more? Thank you.
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Top comment

Hello,

Good question. There are two key things to observe here:

  1. \(\text{argmax}_z y^\top z - f(z)\) means "\(z\) for which the function is maximized". That's a very similar selection criterion as above.
  2. \(z\) is the gradient of \(y\top z - f(z)\) (w.r.t. \(y\))

Hope this helps!

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