You'd probably find me really charming then Peter (although most don't).Personally I think wear adds charm.
You sand the deck (or any surface) at 45 degree angles in a 'X' fashion to remove the cupping. Source; Old man used to own a tool rental shop 'back in the day' and I worked many summers there and our floor sanders were a popular rental item. How thick are your deck boards? If they are 3/4" or less nominal I'd try out the pad sander, otherwise you can probably use a drum sander. Be careful with your grit choices as a 40 grit paper on a drum or floor belt sander (silverline style) will eat deck boards FAST.The reading I've done recommends a plate sander with a 1 inch foam pad between sander and sandpaper for decks. The belt / floor sanders are not that great because the deck boards are cupped and warped. You would have to sand the board flat to get to the bottom of the valley whereas the plate sander with pad supposedly better fits to the warped boards. I've never tried it so we will see.