I am trying to understand the meaning of subgradient precisely. Is the subgradient of a function at point $x$, any linear underestimator of a function that touches the function in only at $x$?
Do you know a more elegant way of putting it?
What is the definition of subgradient in words?
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subgradient
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0Think of it as a hyperplane that separates the point $(x,f(x))$ from the rest of the epigraph. – 2017-01-23
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0Epigraph is still too technical for this purpose. – 2017-01-23
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1Replace epigraph by graph :-). – 2017-01-23