okay: I have to generous with your diction and your intentions. I believe you are trying to say that since 'optimal algorithms for choices exist': 'local maximums can't exist'.

It is very possible to have a optimal algorithm that leads to a sub-optimal (local maximum) because the problem is np hard. Both in math and in life.

"It is possible to commit no mistakes and still lose. That is not a weakness. That is life" - Picard