Maybe the Maya people have some idea or can make a recommendation…
Optimus is a tolerable hardware kludge I’m surprised it works at all. It does work for NVIDIA since they have sold tons of chips. 
Update:
I upgraded from Maya 2015 to Maya 2016 this evening and it works with optirun without crashing. I am also able to use Viewport 2.0 (a feature only available when the graphics card is running).
In the terminal I noticed these lines:
OpenCL evaluator is attempting to initialize OpenCL.
OpenCL evaluator failed to find OpenCL device with vendor NVIDIA Corporation.
So maybe there is still something not working properly. But right now, Maya seems to work with the graphics card.
That is for use of the GPU to run program code for fast vector calculation. This is not strictly needed but does speed up calculation. It may not be supported at all on optimus but even on a normal system you have to add additional CUDA NVIDIA packages to make it work.
Thank you gogalthorp for all of your help.
It seems that Maya 2016 is now up and running fine. I’ve been using it a little over the last two days and have had little problems with it. It crashed once for no apparent reason… but that may have been down to Maya itself, as that can happen on Windows and Mac too.