Counter example: R^1 with a random function. There is no algorithm that can find a global maximum other than checking every point in R^1, of which there is an uncountable number.
Not all cost surfaces are equally likely to occur in real problems...
Also depends on the constraints, linear assignment (i.e. one job to one worker with a big matrix of cost for job to worker and you minimize the sum) has a polynomial complexity solution.
We are not talking about real problems here. Reality is so far from linear, so path dependent, so temporally dependent that by the time you gather 10 data points to try and match some function to the function is already outdated and error prone.
This is infinitely truer for when you try and find absolute maxima and minima and not just local ones.
Sure, some functions have no global maximum. But the comment I replied to claimed a theorem that every utility function on infinite search space has no global maximum, which isn't true.
All models are wrong, some are useful. GP presents an interesting way of framing real life decision making processes. That it happens to not be 100% accurate in all aspects is mostly trivia.
