Timeline for Optimisation over $SO(3)$: is it safe to use a global parametrisation?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 18, 2017 at 18:46 | comment | added | DCM | Taking small steps during the iteration does seem sensible. However, it also restricts how far the simplex can travel for a given number of function evaluations, and isn't always under my direct control: I guess I could restart my iteration if I find the step-size is getting too big... | |
| Nov 18, 2017 at 18:20 | comment | added | DCM | Any and all comments are very welcome! I think my preference would probably be using the exponential map given the choice (I mentioned Euler angles simply because it was the first thing I tried when I coded this up). I have heard of people using the unit quaternions, but I'm not sure that's so different from working in $SO(3)$ without co-ordinates (apart from maybe reducing the number of multiplications slightly). | |
| Nov 18, 2017 at 18:15 | comment | added | Dan Piponi | A small trick I've used successfully: each iteration is a small step. So for each iteration you only need a relative rotation that is close to the identity. Many parameterisations behave well for rotations near the identity. So if your algorithm can be rearranged to work with the increment in the rotation at each step then there is no problem. | |
| Nov 18, 2017 at 17:51 | comment | added | Jarek Kuben | Very non-expert comment: Euler angles are numerically unstable in some area of the sphere (this is called gimbal lock), so I'd think they are not very convenient tool for numerical experiments. As far as I know, this issue is usually resolved by using the double cover $\mathrm{SU}(2)$ (or equivalently the unit quaternions). | |
| Nov 18, 2017 at 17:28 | comment | added | DCM | I should probably say: what I'm really interested in here is whether pulling back to $\mathbb{R}^3$ is intrinsically problematic when using Nelder-Mead for this type of problem (each $f$ actually represents a toy problem where I already know the global minimum). | |
| Nov 18, 2017 at 17:14 | history | asked | DCM | CC BY-SA 3.0 |