It's typical that the Simplex Method implementation exits once it finds an optimum value. However, if I want to find all optima that exist at extreme points (not those that exist along a face), is it possible to walk through them in linear time? In polynomial time?
In my mind, it seems I would need to search through the $n$ decision variables to find one I could move into my basic solution without losing my optimum status. I would then have to back up my changes somehow so I could come back in what I picture to be a backtracking tree search. Am I picturing this correctly?
Can you recommend a source on this topic?