Note: as I mentioned in the post, I’d love feedback of all types—for better clarity, criticism of my understanding, suggestions for how to continue, and places the discussion still seems confused.
This is all a set of mathematical exercises, and probably involves only multiply differentiable models that can be directly solved to find an optimum. This is in many ways a third category of “optimizing,” in Abram’s model, because there is not even a need for looking over the search space. I’ll call this direct solution, since we just pick the optimum based on the setup.
Is this distinction a property of the function we’re optimizing or the algorithm we’re using to optimize it? Is the relevant distinction that there is a unique global optimum? Or that a closed-form solution exists/it takes “constant time”? Or that we can prove a given solution is optimal once we’ve found it?
I think there are optimization algorithms that satisfy some, but not all, of those properties. Personally I don’t think I would create a new entry in the typology for this, and just keep it under “selection”.
I found it a bit confusing that you first reffered to selection and control as types of optimizers and then (seemingly?) replaced selection by optimization in the rest of the text.
Note: as I mentioned in the post, I’d love feedback of all types—for better clarity, criticism of my understanding, suggestions for how to continue, and places the discussion still seems confused.
Is this distinction a property of the function we’re optimizing or the algorithm we’re using to optimize it? Is the relevant distinction that there is a unique global optimum? Or that a closed-form solution exists/it takes “constant time”? Or that we can prove a given solution is optimal once we’ve found it?
I think there are optimization algorithms that satisfy some, but not all, of those properties. Personally I don’t think I would create a new entry in the typology for this, and just keep it under “selection”.
I found it a bit confusing that you first reffered to selection and control as types of optimizers and then (seemingly?) replaced selection by optimization in the rest of the text.