How long has your tank been up and running?
sterlizer may be overkill - before going out and getting one I'd say do 10 - 15% water changes each week, instead of the bigger change every other week. May also be worth doing some water testing (specifically looking for phosphates). You may also want to reduce your feeding schedule a bit: sometimes if you're overfeeding those extra nutrients can feed into algae.
If the tank is relatively new, you just need to get over the algae hump: we all go through it. Diatoms, then hair algae, and then (hopefully) that stuff will all leave you alone.
With corals, also, are you protein skimming? If not, it might be a good idea to give that a whirl.