I'm trying to optimise (to a certain precision) a monotonic function for many points (100+). I know a-priori that the function is continuous, with some parts zero derivative. I know that all points lie within a range [a, b].
My current approach is to sample the range [a, b] with N points, and then find the closest initial point to every desired solution. I bisect every subrange iteratively (and collect output values) until all solutions are converged. I was wondering if there are faster specific algorithms for such a setting. Googling "monotonic function multiple point optimization" doesn't quite help me further, as the results are not at all relevant.