I think this is a very important distinction. I prefer to use “maximizer” for “timelessly” finding the highest value of an objective function, and reserve “optimizer” for the kind of stepwise improvement discussed in this post. As I use the terms, to maximize something is to find the state with the highest value, but to optimize it is to take an initial state and find a new state with a higher value. I recognize that “optimize” and “optimizer” are sometimes used the way you’re saying, as basically synonymous with “maximize” / “maximizer”, and I could retreat to calling the inherently temporal thing I’m talking about an “improver” (or an “improvement process” if I don’t want to reify it), but this actually seems less likely to be quickly understood, and I don’t think it’s all that useful for “optimize” and “maximize” to mean exactly the same thing.
(There is a subset of optimizers as I (and this post, although I think the value should be graded rather than binary) use the term that in the limit reach the maximum, and a subset of those that even reach the maximum in a finite number of steps, but optimizers that e.g. get stuck in local maxima aren’t IMO thereby not actually optimizers, even though they aren’t maximizers in any useful sense.)
I think this is a very important distinction. I prefer to use “maximizer” for “timelessly” finding the highest value of an objective function, and reserve “optimizer” for the kind of stepwise improvement discussed in this post. As I use the terms, to maximize something is to find the state with the highest value, but to optimize it is to take an initial state and find a new state with a higher value. I recognize that “optimize” and “optimizer” are sometimes used the way you’re saying, as basically synonymous with “maximize” / “maximizer”, and I could retreat to calling the inherently temporal thing I’m talking about an “improver” (or an “improvement process” if I don’t want to reify it), but this actually seems less likely to be quickly understood, and I don’t think it’s all that useful for “optimize” and “maximize” to mean exactly the same thing.
(There is a subset of optimizers as I (and this post, although I think the value should be graded rather than binary) use the term that in the limit reach the maximum, and a subset of those that even reach the maximum in a finite number of steps, but optimizers that e.g. get stuck in local maxima aren’t IMO thereby not actually optimizers, even though they aren’t maximizers in any useful sense.)