Dood... You're in luck. I just went through this ordeal a couple of weeks ago and I have the same monitor as you. I try to keep my monitor spotless, but someone got their greazzy palms on my screen and I had to clean it.
The first thing I tried was a special multicoat cleaning fluid with a microfiber cloth that I use on $1k+ camera optics. This is usually the best solution for just about anything with glass on it. Not this time!! Streak.. Streak..
The next thing that I used was some monitor wipes made by Fellowes. I useally use these on my work monitor and they generally do a fine job. Not on this monitor though... Streak...
About now I'm getting desperate because my screen is turning into a huge mess. I tried water.. Just more of a mess. I tried alcohol on a corner of the screen. More of a mess.. I finally gave in and tried Windex. This made the biggest mess of them all!
At this point, my screen looked so bad that I thought I was going to have to pitch the thing until someone came up with straight vineager. I said, what they he!!... I certainly can't make it worse. I first tried it with a soft cloth and it seemed very promising, but it was still a little streaky. I then tried it with Kleenex and it worked beautifully. I even tried some toilet paper and that was a joke because the tp just fell apart as soon as I tried to use it.
Here's what you need... A box of quality Kleenex. The soft and sturdy stuff. Then find a bottle of straight vineager and sit there and dispense the vineagar onto the Kleenex and go to work on it. You'll be amazed. I was!
Now.. Since the Windex just made an aweful mess of my screen, maybe you won't have to use as much Kleenex as I did or work nearly as hard. I must tell you that I probably went through half a box of Kleenex on this thing.
I'm using my monitor right now and it's perfect!! I looked at it in the light from all angles and I don't seen one smear or streak and not one scratch.
Someone also suggested a real Chamois with water for dust and I may do this yet. Make sure and buy a new one though just for your monitor and not use the one that you have for the car. Even the smallest piece of debris will sratch your monitor. That was a tip passed onto me as well..
HTH..
Let me know if you need any other help with this..
Sal