Potatoes do well in containers, so long as the soil medium is light, there is sufficient room, and they are kept watered.
Grow-Box gardening produces wonderful potatoes. Grow-Boxes are containers that are usually open at the bottom, but not necessarily, if they are on a patio, roof, or driveway.
The key to having great potatoes, beyond the three elements I named in the first paragraph, is to feed them properly.
Apply Pre-Plant Mix and Weekly Feed mix to your soil before planting, and thereafter apply Weekly Feed every 7 days until your plants flower.