Suppose there is a convex function, and a certain domain interval. I want to fin

Question

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

Explanation / Answer

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.

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