no there is NO adapter for that!!!
If you let us know what type of inputs you yamaha speakers have then it will be easier to help you.
My guess is that it has RCA jacks (Red and White) like #4 and #5 from the above picture, a headphone style jack, or a mini headphone style jack (as seen on the back of sound cards). I dont think those speakers have optical from looking at that link.
In any event this is what you do:
You can run the audio and video seperately from the back of the PS3!
Video: PS3 -> HDMI -> HDMItoDVI Converter -> Dell Monitor
For Audio use any of the old style AV cords which include:
Composite (3 RCA plugs, yellow,red,white)
SVideo (1 Black SVideo plug + 2 RCA red,white)
Component(5 RCA plugs (3video red,green,blue), (2audio red,white)
Use the RCA audio red,white plugs found on any of these for the audio and just leave the video cables on these plugs disconnected.
PS3 allows you to independently configure audio and video so you can use the hdmi for video and audio, or choose the optical or any of the above listed cables for the audio!!!!
Of course if your speakers only have headphone mini jacks for input then you get an RCA to Mini adapter. But there is NO such thing as an optical converter like you hoped, there may be some high end equipment that does it but your looking at hundreds of dollars just for the converter, for that money you can just buy a better speaker system than those yamahas with an optical input like those already mentioned.
And a quick primer on optical:
It can go by 3 names: Optical, tos-link, SPDIF (Sony Philips Digital Interface)
All refer to the same thing, the cable steve pic'd above.
The reason its called optical is because its a fiber-optic cable and uses pulses of light to transfer digital optical signals instead of digital or analog signals using electric current over metal cables.
Class dismissed hehe