You raise a very good point in that the "formulate the problem the way the solver wants" step is legitimately difficult and full of pitfalls. Simply figuring out the translation can be hard, and even then there are many ways to formulate a problem which are mathematically equivalent but have drastically different performance when fed to the solver.
It really feels like a tools or language problem. Heck, we used to have to manually work out derivatives for continuous optimization problems, but nowadays programming languages with performant built-in autodiff often make this trivial. Removing the manual derivation hassle let loose a flood of cool ideas and applications, even though there was no technical hurdle preventing them in the first place.
Alternate problem specifications is a well-explored area (what is Prolog if not a way of describing problems for a constraint satisfier?), but I wonder how many other neat things are dammed up behind usability problems.
It really feels like a tools or language problem. Heck, we used to have to manually work out derivatives for continuous optimization problems, but nowadays programming languages with performant built-in autodiff often make this trivial. Removing the manual derivation hassle let loose a flood of cool ideas and applications, even though there was no technical hurdle preventing them in the first place.
Alternate problem specifications is a well-explored area (what is Prolog if not a way of describing problems for a constraint satisfier?), but I wonder how many other neat things are dammed up behind usability problems.