Become a troll. Or join up with one. Or sell out to one. Or sell to someone else who wants your patent for other reasons.
There are now a very large number of investors and attorneys who will help you to monetize your patent - provided they think they can make money from it. Almost all of them would be described as patent trolls, more politely known as "non-practicing entities" or NPEs. These are the guys who provide Davids with slings and stones to go up against Goliaths - for a piece of the action.
For some reasonably accurate background on the term "patent troll", check out the Wikipedia entry: http://en.wikipedia.org/wiki/Patent_troll
BTW, you could also offer to sell your patent to practicing entities other than your suspected infringer in the appropriate technological field. Your patent could be an arrow in the quiver of any entity who contests with the large company that you suspect is infringing your patent.
The principle is much the same in any case - trying to determine a net present value of the patent in the marketplace. Making such a determination has little to do with judging whether your invention is worthy as being original and much more to do with judging how much money can be extracted from the broader world of commerce via ownership of the patent.