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What is the state of art gradient based algorithms in convex optimization solving non-smooth piece-wise linear functions? Thank you.

EDIT: It is different from one of my previous post in the sense that here, I am focusing on piece-wise linear functions:D

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There are two cases I can think of (assuming minimization):

  • your non-smooth piecewise linear function is convex, in which case, standard reformulations result in a convex program (or even a linear program), so you can consult a textbook in convex optimization such as the one by Boyd to find applicable algorithms.

  • your non-smooth piecewise linear function is nonconvex; then the reformulation I mentioned above doesn't apply, and you probably need to provide more about the problem structure.

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  • $\begingroup$ My problem is convex. The problem is that, I intuitively think I shall use Nesterov's accelerated gradient method... But the book hasn't introduced that... And I am wondering whether there is even improvements on Nesterov's method to specially tackle convex piece-wise linear problems... $\endgroup$ – user40780 Mar 21 '15 at 0:28

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