Unlike the gradient, there is not "one subgradient of f at x", but any vector \(g\) that satisfies the equation in your screenshot is considered a subgradient. You can see subgradients as touching lines that are always below the function.
For x^2, you can not make a line through x=0, y=0 that is always below the function, so there is no subgradient.
An example of a non-convex function that has subgradients (in some points) is the following:
Q6 2020
Hello for question 6, they say the subgradient is not defined for a concave function
However in the course we saw the following:
I am quite confused on when is the subgradient defined?
Hi,
Unlike the gradient, there is not "one subgradient of f at x", but any vector \(g\) that satisfies the equation in your screenshot is considered a subgradient. You can see subgradients as touching lines that are always below the function.
For x^2, you can not make a line through x=0, y=0 that is always below the function, so there is no subgradient.
An example of a non-convex function that has subgradients (in some points) is the following:
2
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