NCP with `offset`/`multiplier` vs doing it "by hand"

[mhollanders]

Check out this recently revived thread for some unexpected differences between the two parameterisations. It was mostly over my head but I think the auxiliary approach always works as intended, whereas the offset/multiplier approach can have run into some issues. Re: hyperparameters, I don’t think it’ll matter too much there as the funnel geometry happens when there’s parameters on both the left- and right-hand sides of expressions.