I actually have your model ready for you (takes 11 inputs, minimizes one output, maximizes the other):
def model(a,b,c,d,e,f,g,h,i,j,k):
return float('-inf'), float('inf')
No library needed!
If you need more help I would encourage you to provide more detail.
I'm just looking for ML libraries that can optimize inputs for multiple outputs. The ones I've found thus far seem to require knowledge of some function, but the function is the unknown.
Combine and make them one output
The outputs are distinct, so I can't combine them. One has to be as close to 0 as possible and the other has to be as high as possible, and I need to optimize the inputs to do that.
output 1 - c*|output 2|
How about a custom loss function so you have something like loss=y1^2 -y2 for the two outputs? You can use PyTorch and optimize directly for the inputs.
Your are fitting model parameters to make input through the model (function) match the output?
Or you have a function where you want to solve for the inputs that min / max the output?