I hope this is not a trivial or insolvable problem and it’s not too much OT. In case it is, apologies in advance for my poor math skills and feel free to hide the question.

I have a complicated function f (continuous, differentiable) of 4 independent parameters, say f(x,y,z,t) all bounded between 0 and 1: x,y,z,t \in [0,1].

Are there packages able to map the 4-dimensional space to find n sets of \{\hat{x},\hat{y},\hat{z},\hat{t}\}_n where the f(\hat{x}_i,\hat{y}_i,\hat{z}_i,\hat{t}_i) \geq 1? I am not sure if this problem can be recast into a constrained optimisation one as I’m interested in the condition f\geq 1 so I suspect that it might be a different type that I’m not aware of and I hope there might be a library able to help me with it.

## Update

After putting some more thought in it, I think that I can follow this high-level algorithm.

- start with a “Monte Carlo”-like approach sampling the independent variables from uniform distributions
- automatically select the closest points to f=1 to identify the frontier
- use NumDiff to explore the numerical derivatives around the frontier to understand where the area f\geq 1 is located with respect to the independent variables.

It might work, although I feel that a more “educated” approach might be available.