Timeline for Basin of Attraction
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 16, 2015 at 21:42 | comment | added | Michael | It seems you can get a condition from the second-order Taylor theorem in multiple variables, of the form $F(y) = F(x^*) + \frac{1}{2}(y-x)^T \nabla^2 f(z) (y-z)$ for some vector $z$ that lies on the line between $y$ and $x^*$, and where $x^*$ is a local max. If all eigenvalues of $\nabla^2 f(z)$ are negative, you are in business and the smallest magnitude eigenvalue helps give a bound that might be useful. | |
| Sep 16, 2015 at 21:28 | comment | added | Michael | Minor observation: If there is a vector $y \in \mathbb{R}^N$ such that $z_i^Ty>0$ for all $i\in\{1, ..., N\}$, then there is no global max and $\lim_{\theta \rightarrow\infty} F(\theta y) = \sup_{x \in \mathbb{R}^N} F(x) = N$. | |
| Sep 7, 2015 at 18:21 | history | asked | Mkl | CC BY-SA 3.0 |