Timeline for How can we show that if $f$ is convex, then $\liminf_{|x|\to\infty}\frac{x\cdot\nabla f(x)}{|x|}>0$?

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Jan 27, 2019 at 17:05	comment	added	Iosif Pinelis		@0xbadf00d : No, this is not possible, because (i) the $\liminf$ is $>0$, (ii) $\langle\nabla f(x),x\rangle\ge f(x)-f(0)$, and (iii) $f$ is continuous and hence locally bounded. If you have no further questions about my answer, then, I think, any further questions should be asked in another post.
Jan 27, 2019 at 16:36	comment	added	0xbadf00d		Thank you very much for your notes. If $r>0$ is small, is it possible that $\inf_{\|x\|\ge r}\frac{\langle\nabla f(x),x\rangle}{\|x\|}=-\infty$?
Jan 27, 2019 at 15:20	history	edited	Iosif Pinelis	CC BY-SA 4.0	added 1087 characters in body
Jan 27, 2019 at 5:26	history	edited	Iosif Pinelis	CC BY-SA 4.0	added 4 characters in body
Jan 27, 2019 at 5:19	history	answered	Iosif Pinelis	CC BY-SA 4.0