I think you misunderstand my point: in general, optimization problems do not have algorithms that guarantee a (global) optimum. Some special cases exist (eg convex problems), but generally no matter how excellent and bug-free an implementation is, for every general algorithm you can devise a problem where the global optimum is not found.
No, I didn’t. I know your point very well. Indeed, even for the algorithms that guarantee a global solution in theory, and even if such an algorithm is applied to a convex problem, you most likely only obtain an approximate solution within finite time — even this is usually based on the assumption that your code is doing real-number calculation, whereas it really performs only floating-point arithmetic. However, this is irrelevant to the topic discussed here.
We all like to believe that our work matters, but perhaps this is taking it too far
Thank you for pointing this trivial fact out, although it is again a topic unrelated to the discussion.
Thanks.