In convex optimization, if we know the gradient of a function $f(x)$, then is it true that we could always find a way to determine a proper step size in the gradient descent method? When I say "proper" I mean it only need to be proper enough to make the funciton $f$ converge to the optimum.

  • $\begingroup$ You clearly need additional assumptions on the smoothness of $f$ (Lipschitz gradient e.g.) $\endgroup$ – Gabriel Romon Jul 7 at 17:30
  • $\begingroup$ Do you want the the iterates to converge to a solution or the function values to converge to the optimal objective value? $\endgroup$ – xel Jul 8 at 22:48
  • $\begingroup$ Im sorry but what is the difference? $\endgroup$ – Hardy Jul 9 at 8:56

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