*very* Low voltage regulator
The problem is that your 500mV output requirement is rare, so that very few regulators use a reference that is lower than ~1.25V (a few use 800mV). 

One way to get this to work is to amplify the feedback signal using an op-amp. A gain of 3 would allow you to use any regulator with a reference voltage up to 1.5V. 

Edit:

Say your regulator has a 1.25V reference, so you'd normally use a voltage divider RA/RB on the output such that Vout = 1.25V (1+ \$\frac {R_A}{R_B})\$. 

Add a suitable op-amp to amplify the output voltage: 



Vin comes from your output voltage. Say it is 500mV and your regulator has a reference voltage of 1.25V. Vout goes to the feedback input of the regulator (where the tap on the voltage divider goes). 

In general your output voltage will be Vout = Vref (\$\frac {R_G}{R_F+R_G})\$,  so in this particular example we might pick Rg = 10K and thence calculate Rf = 15K.