Extermination is a reasonable and realistic solution to the problem. While I said earlier and still firmly believe that poisoning is not a responsible method of doing so, because of the potential to kill species other than the intended target and I do not encourage animal cruelty- housecats are a bane everywhere they have been introduced. A foul, invasive, destructive species that propogates quickly and obliterates native wildlife. When a feral population has been established as a breeding group, it is not particularly effective to take one cat, have it neutered and then... what, release it again? Many need to be either contained and euthanized or, if initial capture is difficult (it usually is), they need to be actively euthanized whereever they are encountered.
Your house pet is your house pet... keep it in your house and it'll be fine. Let it loose to terrorize the surrounding area and there is nobody to blame but yourself if it ends up poisoned, hit by a car(unintentionally I hope), captured and euthanized by the local vet or shot as the menace that it is.
"Genes, Like Leibnitz's monads, have no windows; the higher properties of life are emergent... And once assembled, organisms have no windows." - Edward Wilson, Sociobiology