Can someone please explain the significance of the subscript 2 on this picture?

Asked Jan 15 '22 at 06:22

Active Jan 15 '22 at 06:22

Viewed 34 times

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Does the subscript here refer to the L2 norm? In the right hand side, are they saying that this is are squaring the square root of the difference in squares? Is convergence here reffering to the real minimum of the function "f"?

Is this correct?

Thanks!

asked Jan 15 '22 at 06:22

stats_noob

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Yes, yes & yes. I do not think the hypotheses are enough to ensure that a minimiser ($x^*$ above) exists. – copper.hat Jan 15 '22 at 06:33
Thank you for your reply! Why do you think that? I would be curious to hear your thoughts! – stats_noob Jan 15 '22 at 06:44
$f(x) = x$ has no minimum. There is often a condition such as the Hessian satisfies $f''(x) \ge \mu I$ for some $\mu >0$. – copper.hat Jan 15 '22 at 06:45
Thank you for your reply! I wonder why this point wasn't brought up here? – stats_noob Jan 15 '22 at 06:49

Can someone please explain the significance of the subscript 2 on this picture?

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