Is there a divide and conquer algorithm for optimizing weakly unimodal continuous functions?
Adding more details:
My function has a flat line on the left and right and then there is a global minima in between but this global minima repeats for a while on what would seem like a straight line. To the left of the minima and right of the flat line on left, the behavior is monotonic decreasing. To the right of the minima and left of the flat line on right, the behavior is monotonic increasing. Also, the function is a positive function that is it's range is always >0. In addition, the function is defined only above zero. i.e, it's domain is always >0.
I see the main issue being that the initial bracket of three points may not be ideal. If the initial bracket was ideal, then does golden section search converge to optimal solution? Or is the issue bigger-even if the initial bracket was ideal?