@CarlLange :facepalm:

I am looking to minimize a black-box vector function f. It has a real vector input of high dimension (on the order of 100 - 1000) and a scalar output. It's implemented as a compiled function for efficiency.

FindMinimum does indeed work with vector functions, FindMinimum[f[x], {x, init}] where init has the same dimension as x, indicating to FindMinimum that x is a vector.

But now I would like to constrain some of the components of the vector x. They must not change from their initial value. I want to be able to easily adjust which components to fix. What is a good solution for this that is easy to write and does not compromise performance?

I can do something like FindMinimum[{f[x], Indexed[x, i] == init[[i]], ...}, ...] for many different i, but this seems like a pain and I think it does affect performance.

I'll post a main-site question.

Definitely don't have the knowledge to help you, but kudos on the great question!