Parameter studies are built to "hunt" for a specific value. Unfortunately that means you can't minimize or maximize (true optimization). This would be a great feature so I'd highly recommend adding to my enhancement request in the solidworks customer portal. Here is the eSR: 1-3483032429
The parameter study tool is WYSIWYG so there is no method to take the derivative of the goal. You could try monkeying with an equation goal but I don't think you're going to get what you're looking for.
My suggestions would be to use the 2013 parameter study tool to do a parameter sweep. Let Flow Simulation go through several dimensions or flow conditions and give you the outputs. From there you should be able to find the trends that lead you to what dimensions that minimize your parameter or you might find it with the parameter sweep tool if you run it through the min/max for those parameters.