Mac mini with NEC PA271W-BK anyone?

You can connect it via the Thunderbolt (TB) connection by way of aDVI to Mini DisplayPort adapter. I used the this method to connect a ASUS PA248Q and a 2012 MacMini.

Mini DisplayPort to DVI Adapter

Now if your monitor requires a dual-link DVI like my 30" Dell to connect it you might need a powered DVI to Mini DisplayPort adapter. Basically it has both a Mini Displayport and USB cable (for power) on one end and DVI on the other. This allows the monitor to get the full resolution that dual-link DVI allows.

Mini DisplayPort to Dual-Link DVI Adapter

The Mini Displayport is compatible with thunderbolt so the connector are essentially the same. The only thing you'll need to remember is since the monitor is not a true TB display it has to be at the end of any TB daisy-chaining you might do.

This also allows you to leave you HDMI open for an alternate monitor if needed.