Timeline for Fix positive $t$. Construct $a_n \in \mathbb R^n$ such that $(\inf_x \|x-a_n\|_2 + t\|x\|_1 )/\min(\|a_n\|_2,t\|a_n\|_1) \to 0$
Current License: CC BY-SA 4.0
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| Oct 14, 2022 at 6:21 | comment | added | dohmatob | This is really interesting and insightful. Thanks. | |
| Oct 14, 2022 at 4:51 | comment | added | Iosif Pinelis | The case $t\to0$ has now been considered at mathoverflow.net/questions/432410/… | |
| Oct 13, 2022 at 18:11 | comment | added | dohmatob | Sorry, indeed what i meant was $t \to 0$ with $n \to \infty$. I'll make a separate question. | |
| Oct 13, 2022 at 18:10 | comment | added | Iosif Pinelis | @dohmatob : It is now shown that $K\ge M$ for all $t\ge1$. It is more sensible to consider small $t$. | |
| Oct 13, 2022 at 18:08 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 13, 2022 at 6:09 | comment | added | dohmatob | Thanks for the answer. Do you think this would if $t$ were now a sequence going to infinity with $n$ ? I can make this into a separate question. | |
| Oct 13, 2022 at 6:04 | vote | accept | dohmatob | ||
| Oct 10, 2022 at 23:04 | history | edited | LSpice | CC BY-SA 4.0 |
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| Oct 10, 2022 at 21:41 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 10, 2022 at 21:34 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 10, 2022 at 21:29 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |