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The equality holds if both A and B are convex. Does the quality still hold if A is continuous differentiable but nonconvex and B is convex? Or put any way, what additional conditions are needed on A if A is nonconvex, such that the equality still holds?

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    $\begingroup$ Take a look at Corollary 10.9 of Rockafellar and Wets' Variational Analysis $\endgroup$
    – ProAmateur
    Commented Aug 6, 2019 at 5:31
  • $\begingroup$ Thanks, that's very helpful. $\endgroup$
    – jsmath
    Commented Aug 6, 2019 at 14:16
  • $\begingroup$ But, is the definition of subdifferential on page 301 the same as a typical definition: g is a subgradient if $f(x)-f(x_0) \geq g(x-x_0)$. In particular, is 8.8 part (b) correct? I don't see how it is correct. $\endgroup$
    – jsmath
    Commented Aug 25, 2019 at 22:57

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