What is the optimal brewing technique for extracting caffeine? I was wondering what process, or processes, would yield the highest caffeine quantity at a fixed drink size (Say 200ml).

Assuming the same variety of bean, same roast, same quantity, same water temperature and same extraction time.
I think the answer to your question is generally going to be espresso.

Brewing process all comes down to pressure, temperature, extraction time (water contact time), possibly agitation and filtering. I may be missing a variable, but all the methods of brewing are just mixing of those variables. If you fix all but one variable, you'd have an answer for any given equation.

All of these things are ultimately affecting the solubility of the caffeine in the coffee.  Since espresso is one of the few brewing methods to affect pressure (and generally uses the greatest pressure) it's going to be the winner.  Increased pressure means increased caffeine solubility.

From wikipedia you'll note the two major factors affecting solubility are temperature and pressure.  You'll also note that dissolution doesn't always happen instantly; rates may vary based on conditions.  By increasing pressure during brewing my guess is that the rate of caffeine dissolution is increased.  making it more efficient for short brewing times.