Cite Formal Definitions of Standard Problem in Thesis
It is probably best to err on the side of completeness as long as you don't get so pedantic that you can't be understood. Some people who later read your work will appreciate those citations, even if your committee doesn't need them. Appendices/annexes are good for including some of that sort of thing. 

But if you rely on a different formulation than the standard it might be especially useful to be complete. You don't, likely, need to chase the full history back (though it might help situate your work), but at least the immediate ancestors to your work. 

Complete, but not pedantic. A balance. 

And of course, your dissertation advisor has the best and most relevant advice on this. He or she needs to be happy.