I was looking at justification as to why the simplex method runs and the basic arguments seem to rely on the follow:
i)The optimal solution occurs at some vertex of the feasible region (CPF points)
ii) There are a finite number of CPF solutions.
iii)If we are at a CPF solution and any adjacent CPF solution has no better value then our solution is optimal.
I'm good with the first two, however I'm unsure how to prove the third part and can find no proof of it.
I can see how to approach it and I believe that the proof will rest on the convexity of the feasible region. I'm just unsure how to prove this is full generality.
Thanks for any help.