I found in the release notes from scipy to version 1.9.0 the following about the optimisation module, in the section "scipy.optimize improvements", 4th point:
Add a vectorized parameter to call a vectorized objective function only once per iteration.
However, I already checked out the documentation for such parameters (for the minisation function and minize_sclar) and couldn't find any hint for such a parameter. While searching in the internet I only found some posts concerning some suggestions or GitHub-issuses to implement such a thing (or workarounds for that).
Where is this parameter to find and can I use it?
Those notes have a more specific note for scipy.optimize.differential_evolution. That parameter is explained there. I've also come across it in other SO questions, but I don't recall which functions use it.
Basically for functions that allow it, you can write an objective function, or other callable (jacobian, boundary?), in a way that takes a 2d array of values. Normally the function just takes a 1d array, the current "state". But with "vectorized=True", the function should be prepared to accept a set of "state" array, and return a value for each.
So instead of calling the objective k times to get a range of value, such as when calculating a gradient, it can call it one, with a (n,k) argument, and get back all k results with one call.
I tried to explain how solve_ivp uses this at