I have an ASUS Zenbook Prime UX32VD-R4002V with NVidia GT620m and Optimus works flawlessly, both in Windows 7 and Linux Mint. Most games and demanding software switch to NVidia, HD4000 is used only for bare desktop and browsing. There are other issues with this ultrabook but Optimus is not one of them. Both DirectX and OpenGL work on both chips, output via HDMI works from both of them and I can even use CUDA in After Effects CS6 by adding 620m to the list of supported cards. The OP's experience is probably constrained to his particular model.
I have the same notebook, and my only complaint is that quite often the notebook monitor doesn't switch on until I connect or disconnect an external HDMI monitor. A pity.
I don't have that problem - it works flawlessly all the time. I am using Amazon basics HDMI cable connected via HDMI switcher to the external display (with the desktop, Chromecast and Tronsmart Android stick occupying 3 more HDMI inputs). Try perhaps another HDMI cable?
I think that's something with my machine, but never wanted to wait for a repair. BTW the HDMI is not a problem: The laptop monitor is often not working when I boot the pc up without any external monitor. But then, attaching one, it will start working.
