First of all you should be careful not to be mixing digital and analog signal. In your case better use a - display port to hdmi adaptor - ( not converter an adaptor is enough). Try to avoid chain connections cause as novuake said in theory they work but in reality the power of the video card and the wire of the cables vary so you're taking a 50 /50 risk it will not work.
In my experience I tried display port to dvi and then convert that to vga didn't go well
. Also tried mini display port to dvi to hdmi it was low quality and some times not recognized by windows and to use it in lunix was near to impossible. So as I said is best to try just one adaptor at the time.