Does YALMIP run in Octave?

Yes, but there are not many solvers available.

Additionally, YALMIP appears to run much slower on Octave. In particular the command sdpsettings is excruciatingly slow in Octave (a factor 100) so you must define it and the re-use it in any call to optimize. Note that if you do not supply an options structure to optimize, a call will be made inside optimize to sdpsettings to create one anyway, so do not omit it.