You may have some luck with a HDMI to DVI converter cable, though you may also have intermittent luck or no luck. Your monitor may need to support HDCP (High-bandwidth Digital Content Protection) via the DVI port.
Also DVI does not support Audio, if your monitor has speakers it also likely has an audio jack (Head phone connector) which will receive audio from the analogue out, unfortunately your PS does not output audio in this way and you would need to convert an Optical signal to an analogue one with a device called a DAC.
You may already own a DAC if you have a HiFi with Optical in.
So in short, if your monitor has the capability a cheap cable will get the picture working but you will still need to sort the sound out.
Your best...