Find the max of a convex function in fewest samples Suppose there is a convex function, and a certain domain interval.  I want to find the max of this function within the interval.  The goal is to minimize the number of times the function is evaluated, because evaluating it is expensive.

I can think of a naive solution involving evaluating the function at two points of the interval (thereby partitioning the interval into three sub-intervals) and discarding the edge sub-interval of the point with the lower function value.  But, I am not sure whether it's optimal.
As the function $f$ is convex, its maximum value in interval $[a,b]$ is either $f(a)$ or $f(b)$.  Otherwise, it will violate Jensen's inequality.