I guess not employability as much as hoping someone will pay me to solve problems with mathematics with ideally some interesting problems thrown in. I majored in pure and applied mathematics and I am fully aware the no one is going to ask me to do functional analysis for cash, but it would still be nice to do some sort of applied mathematics for money.
amusingly functional analysis is really important to convex analysis and optimization so yes if you have a phd/masters (maybe) you can definitely get - probably a giant company - to pay you to do functional analysis.
I've seen at least one or two companies working on optimization at least here on HN. I'd take a guess that Gurobi is one option, and I saw SigOpt post a listing on the recent "Who's Hiring?" thread. Google seems to also do a lot of optimization related work as well. I'm in the same boat, though I was stronger in CS during my studies. The background is useful, but you will only ever use bits and pieces of it at opportune moments.
