Timeline for Is a function of several variables convex near a local minimum when the derivatives are non-degenerate?
Current License: CC BY-SA 4.0
6 events
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| Jul 29, 2020 at 21:20 | comment | added | Mateusz Kwaśnicki | @WillieWong and Asaf Schachar: Thanks! I edited this into the answer (and also reduced the degree from 6 to 4). | |
| Jul 29, 2020 at 21:19 | history | edited | Mateusz Kwaśnicki | CC BY-SA 4.0 |
added 135 characters in body
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| Jul 29, 2020 at 17:11 | comment | added | Willie Wong | @AsafShachar: if $f$ is a homogeneous polynomial, it is equal to its taylor polynomial of that degree, and hence if $v = (x_0, y_0)$ up to some numerical constant $d^6f(v,v,\ldots, v)$ is the same as $f(x_0, y_0)$. | |
| Jul 29, 2020 at 16:40 | vote | accept | Asaf Shachar | ||
| Jul 29, 2020 at 16:40 | comment | added | Asaf Shachar | Thanks. Just one question: Why does the fact that $f$ is a homogeneous polynomial of degree $6$ imply that $d^6f$ is non-degenerate? Can we deduce that without explicitly computing $d^6f$? | |
| Jul 29, 2020 at 15:18 | history | answered | Mateusz Kwaśnicki | CC BY-SA 4.0 |