Dear all,
I have some confusion on the definition of Single-Peaked function. Can anybody tell me the official definition of it?
It is intuitive to understand "Single-Peaked". However, what if the function has a flat part with its level lower than the peak? Can we say this function still Single-Peaked?
In other words, do we require the strict monotonicity on both sides of the peak for it to be "Single-Peaked"?
Thanks in advance.
My guess would be that a single peaked function would be one of which has only 1 maximum value. An example of this would be an inverted quadratic, a cubic with no points of inflection or even an inverted quartic with a point of inflection. This could extend further when looking at the function that generates the bell curve for a normal distribution.
Maybe google knows?
Thank you very much for your informative reply!
Along the line of your answer, my question is:
Given the function has only one global maximum, if it has a flat part somewhere else other than the only "peak" point, would we still count it as the "Single-Peaked"?
Equivalently, do we require strict monotonicity on both sides of the unique global maximum?