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Oct 11, 2016 at 3:35 comment added Nawaf Bou-Rabee Thanks for your clarification and for sharing this interesting paper, even though its assumptions may be tricky to verify in practice.
Oct 11, 2016 at 0:55 comment added Cristóbal Guzmán Just to clarify: the method does not require arbitrary approximation to a Lipschitz convex function: $\epsilon$ is a parameter, which may be large or small. To my understanding, even deciding convexity is a hard problem, so there is no way to computationally verify almost-convexity either. The natural application of this setup (and the only one I am aware of) is a convex Lipschitz objective and optimization via evaluations with additive noise (so-called stochastic zero order convex optimization).
Oct 9, 2016 at 17:44 comment added Nawaf Bou-Rabee How does one verify that a given function satisfies their hypotheses, i.e., can be approximated arbitrarily/uniformly well by a Lipschitz, convex function?
Oct 9, 2016 at 14:48 history answered Cristóbal Guzmán CC BY-SA 3.0