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”.
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”.