Optimising for many points in a monotone function

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.

• I don't understand the problem you are trying to solve. I don't know what "optimize...for many points" means. I don't know what "find the closest initial point to every desired solution" means. Can you edit your question to specify the problem more clearly? One format that might help you structure the problem specification is to describe the inputs to the algorithm, and the desired outputs.
– D.W.
Sep 23, 2022 at 5:27
• Also, please describe how the function is provided. Do you only have a black-box oracle for it, or do you have a mathematical expression for it? What properties does it have? Is it differentiable? Do you know how to compute the first and/or second derivative? Is it a function $\mathbb{R} \to \mathbb{R}$, i.e., one variable to one variable? Please edit the question to specify these details.
– D.W.
Sep 23, 2022 at 5:28